For somewhere to stay overnight, you should look into San Luis Obispo! It's pretty much the largest and most well-known city that's half way in between San Francisco and Los Angeles. Look into The Madonna Inn there. It's a world famous hotel and a trip to visit because all of the rooms have different themes and the garden is very whimsical.  This is close to Hearst Castle.

While looking into San Luis Obispo, there are other really cute beach towns around it, too, that you can look into -- Avila Beach, Morro Bay, and Baywood-Los Osos.

If you like wine, check out the city of Paso Robles, which is more inland and full of wineries.

A little further north of SLO, check out Big Sur. It's one of the most beautiful places I've ever been! Be sure to stop off at Julia Pfeiffer Burns State Park for a little hike and great views!
Santa Cruz is also awesome.  There's the Santa Cruz Beach Boardwalk.  A little further up is Monterey and Carmel.  The Monterey Bay Aquarium is really cool.  Pescadero State Beach is one of my favorites.  There are actually tons of beaches that you can turn off on close to there, just look for the signs.

Have fun! :)

The route 1 drive north is amazing and definitely what you want to do. Good stops include Santa Barbara, Big Sur, Santa Cruz, and Carmel/Monterey. Any of those would be good for overnights, especially Big Sur if you want more nature over cities. If you happen to be in Big Sur on an overnight, hit up the hot springs at Esalen at 1 AM, make sure to reserve that morning. It's a magical, unique experience - hot springs in the middle of the night overlooking the Pacific. More info here: http://www.esalen.org/page/public-night-hot-springs-access-831-667-3047 

I second David's recommendation.  Some in between spots that you might consider:

Pismo Beach or Morro Bay. If you have time you can hop inland a bit for some great wine tasting near San Luis Obispo (aka SLO).

Near Hearst Castle is a spot where elephant seals lie on the beach.  An interesting stop for sure, and doesn't take much time. http://hearstcastle.org/plan-your-trip/area-attractions/elephant-seals/

The drive is beautiful along the coast... but depending on what time of year it can definitely be colder than many people would expect and often overcast, so be prepared.  

Also, give yourself plenty of time for the drive, it can often take much longer than googlemaps or navigation systems will tell yo, especially on weekends. Enjoy your trip!

I think 2 or 3 days is WAY too short for a drive from LA to SF. There is so much to do and see that you'll wish you budgeted more time for the drive. Chances are with that little time, you won't be able to do much more than get out the car, snap a few pics, and get back in the car. Probably not the best way to enjoy what is one of the best drives on the West coast. 

I recently did the reverse drive with a couple of friends and here are a few places I think you should definitely spend some time at. 

1. Have lunch at the restaurants near the Pebble Beach Pro Shop. The facilities there are beautiful and the view from the restaurants are breathtaking. 
2. Spend a night in Santa Cruz. The hotels there are pretty cheap and it's a great beach town to spend a night in. The night life is also pretty active due to it being a college town. We had a blast bar hopping around downtown. 
3. Check out Pfeiffer Beach Day Use Area in Big Sur. It's a hard to get to beach (small windy roads), which makes it less crowded. It also has some big rocks to climb onto for some gorgeous views of the ocean and nearby cliffs.
   

Those are probably my top 3, but if you had more time, I'd add a few more recommendations. 

Hmm... You might try Solvang--a Danish village right in California. It's on your way from LA to SF; if you're taking Hwy 1 then veer off to the 101 after you pass Santa Barbara. What's interesting is I'm sure the town is "touristy"--yet I don't know any Californians who've been there (and very few even know it exists), nor do I know any tourists who have visited it while in California. Of course, if you've actually been to Denmark, this village may not interest you. Here's the town's website: http://www.solvangusa.com

Or, if you want to stay on Hwy 1, you'll pass through Lompoc, which really is only known for its Air Force base--but, if you pass through there before sunset, take Ocean Ave all the way down till you hit the ocean, right by the Amtrak tracks. From there you can watch the most incredible sunset on an almost secluded beach. It seriously was one of the most beautiful sunsets of my life. However, other than that, there really isn't anything to do in that town, and a very limited number of restaurants and hotels.

When you get to the Bay Area, it will be expensive to stay anywhere. But here's a hidden gem if you're up for tent camping: Sanborn County Park in Saratoga is up in the mountains and really peaceful. I think it's about $14/night, but spots fill up fast. Here's the website: http://www.sccgov.org/sites/parks/parkfinder/pages/sanborn.aspx

I also agree with the previous answers, especially Big Sur. There I recommend Pfeiffer State Beach. 

Enjoy your trip!

I do the LA - SF drive via the 101 quite often and Debbie's recommendations are spot on. San Luis Obispo makes a great overnight stop since it is exactly halfway. I usually stop for coffee and lunch / dinner somewhere in downtown Santa Barbara but most recently I find the shops and cafes around Coast Village Road in Montecito to be much more charming and local. 

Another alternative is to take the inland route and stop for a day in Yosemite National Park, which is about 5 and a half hour drive from LA to inside the valley and less than 4 hours from SF. It's one of the best national parks and absolutely beautiful. In winter you may have the park to yourself. Some roads may be closed so check ahead but the west entrance should be open. If you time it right you can be at the park before sunset and have the morning to explore. I recommend staying at Yosemite Lodge at the Falls in winter time. There are some short easy hikes great for daytrippers. 

Definitely take Highway 1 along the coast (as opposed to the 5 freeway through the middle of the state) and make your first stop in Santa Barbara (one hour + 10 minutes from L.A.)  - at least for lunch (try La Super-Rica Taqueria), or, even better, overnight (stay at Four Seasons Resort The Biltmore Santa Barbaraif you can swing it, or The Canary Hotel Santa Barbara (more city central.) Wine tasting in the area is really fun. Then do the bulk of your driving and get up to Big Sur to spend the next night. Post Ranch Inn is Heaven on Earth, but it's also crazy expensive. A cool cheap option is the Glen Oaks Big Sur. I actually wrote an article for the LA Times mentioning some of the above: http://www.latimes.com/travel/la-tr-highlow-20100404-story.html

Have a great time!

Just had a friend stay Ragged Point Inn & Resort. They highly recommended it. Much less expensive than other alternatives in Big Sur, but not sacrificing quality.

Santa Barbara is lovely.  It would make a great stop for the first night.  Great restaurant scene and a beautiful views.  Second night stay near Pismo Beach if you want to be on the water or look into San Luis Obispo if not.  Definitely do Hearst Castle and take plenty of time to drive the road through Big Sur.  If you can stay a third night on the road, Carmel is great!

After seeing Hearst Castle, I'd advise going and spending the night in Monterey.  It is about an additional 2.5 hours drive up highway 1.  From Monterey, you can explore Carmel, Point Lobos, the Monterey Bay Aquarium.

I would recommend highway 1 and Big Sur, absolutely spectacular scenery, feels like the edge of the world! Also loved Carmel by the sea, beautiful beach.

I would recommend a night in Santa Barbara then Cambria (not far from Hearst Castle) and then a third night in Big Sur. There are some other great places north of that but I usually cross over after Big Sur toward San Francisco.

I am not sure what your budget is for the trip. If you are trying to save money I'd suggest staying at one of the Inns near the waterfront in Santa Barbara. If you have a little more money you can stay Hyatt Santa Barbara to be right across from the beach. In Santa Barbara you can hike, bike, kayak, paddle board (cheap rentals in the waterfront/harbor areas) and more. Just off the beach is The Funk Zone with an urban wine (and beer) tasting trail. On State St you will find shopping and restaurants galore, one of my favorite spots for dinner is Jane.

In Cambria the Cambria Pines Lodge has great deals (look up coupons online). There is a delicious restaurant there called the Black Cat Bistro - I would highly recommend it. On your way North about 15 miles after Cambria is the Elephant Seal Vista Point - DON'T MISS THIS. It is incredibly cool and you really only need to take 5 minutes to pull to the side of the road and see the sights.

In Big Sur I have only camped so I can't give any recommendations there for hotels (I believe they are all pretty spendy) - but a lunch stop at Nepenthe is fun for beautiful cliffside ocean views. 

Big Sur also has Julia Pfeiffer Burns State Park and McWay Falls which are must sees there.

Enjoy your trip! It will be lovely!

Tourists like to check out Big Sur and Pebble Beach.  Checkout the Fisherman's Warf there in Monterey.  There is a really awesome sandwich place that I really miss called Compagnos.  There is also a really amazing greek restaurant downtown.  The Presidio of Monterey is there (aka The Defense Language Institute.)  That is where all branches of the US train their linguists.  They have an outdoor mall in Monterey but it's not worth going to if you are driving through.  Definitely check out Big Sur, The Fisherman's Wharf and get a sandwich at Compagnos.  There is an aquarium too.

Compagno's Market & Deli

Directions

Address: 2000 Prescott Avenue, Monterey, CA 93940
Phone:(831) 375-5987

Take Highway 1 up the coast. You'll past Hearst Castle on the way. Big Sur is a MUST. It's so beautiful, and there's plenty of state parks to check out if you have the time (Julia Pfeiffer Burns State Park, Andrew Molera State Park, etc.). Continue driving north and you'll eventually hit Carmel, where Point Lobos is a popular park. Monterey has plenty of hotels to stay at. I recommend finding a place on Airbnb. Pacific Grove (which borders Monterey) is a great, local page. You can walk on the beaches at Asilomar Beach. After Monterey, continue to drive North. After after 2.5 to 3 hours you'll come to San Francisco/ Bay Area. Plenty to do there, and lots of places to see! 

David basically nailed it with his locations...was about to write basically the same answer.