If you are staying in the city and heading to Napa, I would definitely recommend stopping by Marin Headlands to get a great view of the bridge from the north side. It's a great lookout point and makes for great pictures. This stop can take you 5 minutes or 5 hours, depending on if you want to hike, drive through it all or just enjoy the great view and keep going. Assuming the 18th and 22nd are travel days - leaving you less than a full day, I wouldn't try to fit too many things into your itinerary. I think the magic of San Francisco really shows through when you have a bit more time to explore. The touristy things are obviously popular for a reason, but it's the random streets and accidental findings of new neighborhoods that showcases how great this city is.
However, if you still want to see multiple things; Marin County is super close to the city (just on the other side of the bridge) and there you'll find Sausalito with great restaurants like Bar Bocce, Mount Tamalpais which is great for hiking and offers amazing views at the top, Muir Woods National Monument and beaches like Stinson Beach , Rodeo Beach and Muir Beach.
Monterey and Carmel are gorgeous and very scenic although with limited time I would skip unless it's a bucket list item. It's much more relaxed and not as much to do although the views themselves are gorgeous. You should also factor in that getting there often takes longer than the gps predicts because there is only one road and there's often traffic.
For places to see in SF:
- Haight-Ashbury - famous intersection and fun, crazy neighborhood
- Mission District - authentic mexican food and lots of new food places popping up everywhere. For food check out La Taqueria for a burrito dorado - it's the best burrito I've ever had. For bakeries check out Tartine Bakery and Craftsmen and Wolves.
- Hayes Valley - super cute neighborhood for nice restaurants and some light shopping. I love O-toro for sushi, 20th Century Cafe for the best honey cake (OMG it's delicious), and Chantal Guillon for macarons.
- Twin Peaks provides a great look out and view of the entire city
- Golden Gate Park is a must see!
- Alcatraz is fun to see in my opinion - especially if you want to do touristy things. For this, you will need to buy tickets in advance, online or over the phone.
A great place to eat is Kokkari, this is an all around amazing restaurant - their lamb chops, octopus and whole grilled fish can't be missed!
For a fun, new place I really enjoyed The Barrel Room in the Financial District.
There is so much to see and do, but I think this covers all the can't miss things! Hope this helps and if you want any more in depth reviews of restaurants or a custom itinerary you can check out my blog, Eat and Escape.