Hey Mark, 

I agree with everyone else that LA is massive. It can be a challenge without a car but totally doable--especially Hollywood and Downtown. The west side is a bit trickier. I'm not sure what you're into so I'll try to give you a few unique recommendations from around the city.

Los Angeles Arts District is an old industrial area that has grown into small neighborhood with lots of street art and cafes.

Grand Parkis right in the heart of Downtown and worth checking out.

Silver Lakeis considered the hipster area. Lot's of cafe's and various vintage shops.

The Getty Center was already mentioned by I second it. Nice art collection and incredible views.

Abbot Kinney Blvd is an interested section of Venice with a very trendy vibe to it. 

Venice Canals are nearby and make for a beautiful walk. It was originally meant to replicate Venice, Italy but now it's residential.

Main Street in Santa Monica has maintained an old beach town vibe better than the rest of Santa Monica. It's also right near the beach.

The best shopping can be found Westfield Century City and The Grove .  You can go to the Griffith Observatory for the best views of LA.  Take a day trip to Catalina Island .   The LACMA is great if you're into art, or also try the Getty Museum .  Not only is the art great there, but they also have sweeping views of LA and entry is free.

Hey Mark,

The other posts are awesome for sights to see so I'll add in some foodie places to go.   If you're traveling south (near disneyland) try checking out Honey & Butter Macarons for some cute macarons. Santa Monica Farmers Market for some good eats and then rent a bike and ride down the boardwalk to Venice Beach Boardwalk. Pink's Hot Dog for some iconic hot dog goodness. The Stinking Rose - A Garlic Restaurant for some garlic awesomeness.  Catch a concert at Walt Disney Concert Hall 

Lot's to do there. Check out places like http://www.laweekly.com/calendar/ to see whats going on while you're there too! 

Hi Mark! You can hit up L.A. Live Way. The Nokia Theatre LA Live, The Grammy Museum and a handful of restaurants are there. It's located right by the Staples Center, so you can catch a game/show/event and then head over to the plaza for some food and fun! 

Go to Amoeba Music in Hollywood

Since I'm a musician, I'll spend a lot of time in Hollywood checking out the guitar shops (a visit to Carvin Guitars and Pro Audio is a must for me, but most people won't care!).

But aside from that, I love the La Brea Tar Pits ... it's this wild, primordial place right in the middle of concrete and steel. Such a cool reminder that the earth is alive, even right where you least expect it to be.

Hey Mark!

Like Tiana mentioned below, LA is HUGE and it's very hard to get around without a car. However, I've compiled a list of Top 10 Low-Budget Things to do in Los Angeles on my blog. Here's the brief list. If you'd like to read more/see pics, click on the link above :)

1. Santa Monica Pier

2. The Getty Center and/or the Getty Villa

3. Hollywood Walk of Fame

4. Watch the sunset at the Griffith Observatory

5. Go out in Hollywood

6. Hike to the Hollywood Sign

7. Go to the farmer's market at The Grove

8. Buy/see all the street art at Venice Beach

9. Go on a trail in Malibu Beach

10. Point Dume State Beach

Hi Mark, 

It really depends on where in LA you are staying. LA is a big place. More details about your interests would help but ill try and give you my best answer. 

Hollywood Walk of Fame if you want to see the famous stars and handprints and lots of touristy things.

Santa Monica Pier is great for shopping, site seeing and beautiful views and has rides and carnival things for kids. Also the top of the Ferris wheel is a great place to take photos.

The Grove is an outdoor mall with celebrity sightings, lots of shopping, dining and a movie theater.

Universal Studios Hollywood if you love movies, theme parks and fun this is a great place for the whole family and to see behind the scenes of the movie and tv business.

There are some great recommendations here! I would add, not to miss the LACMA - such a great museum. Very interactive and more entertaining than your average museum!

Spend a Saturday or Sunday afternoon at the historic Olvera Street esp if you want to get a feel for "Latino LA". For a quick bite, grab some taquitos with green sauce Cielito Lindo or grab some churros filled with dulce de Leche (caramel) Mr Churro.  Union station is just across the street for additional "old LA" adventure. 

One really fun thing to do if visiting Los Angeles is to become a visitor to a TV Show recording or possibly getting selected as a contestant on a game show. The best way to schedule free tickets in advance is to use this site:

http://www.on-camera-audiences.com

enjoy your trip to LA!