LA - Recommendations?

Downtown (i.e., near your hotel):
Water Grill is expensive but great seafood
Patina is expensive but just great generally
Whatever Patina's sister restaurant next door to the downtown library is called, it's not cheap but less expensive than Patina and still very good
Ciudad is good upscale South America-inspired food
Philippe's is fantastic French dip
The Grand Central Market is great for lunch, a whole variety of foods, "ethnic" and otherwise
There are some great places in Chinatown and Little Tokyo, which are both walking distance from your hotel, as is Olvera Street (which is also close)
The restaurant in Union Station (the downtown railroad station) is pretty good and a great setting. Nick & Stef's is a good downtown steakhouse.

In Beverly Hills, there is Spago, which is very expensive and a bit of a scene, but the food really is great.
Shiro in South Pasenda is one of my all-time favorite restaurants. If you go, get the catfish.
Can you give us some idea what kind of budget or what kind of food or dining experience you enjoy? LA has some great haute cuisine places, but also some of the best "ethnic" foods you'll find anywhere in the U.S. Amazing Chinese out in San Gabriel, really good Indian (although not quite up to London's standards in my opinion), Korean, various Southeast Asian, Iranian, Mexican Ethiopian/Eritrean, etc. Most are available in both relatively upscale varieties and the down-and-dirty cheap and tasty varieties.

My favorite restaurant in LA is Lucques. Lawyerdad has good recs as well, although to anybody who is not LA, the whole Wolfgang Puck scene is really played out.

Lucques is excellent. I also agree that the Puck star-factor thing is played out, but I still love the food at a couple of his restaurants.

Honestly, I don't like Spago because it took over the space that was once The Bistro. By coincidence, the Bistro was the first place that my mother ever met my Grandparents, and also the first place I ever introduced a serious girlfriend of mine to my own mother. It was quite good, but eventually quite dated as well. I used to like Chinois a lot, but talk about dated.

As long as we're bring up Lucques (which I love) I should mention that Suzanne Goin's other restaurants, The Hungry Cat (seafood) and AOC (wine, tapas, charcuterie) are both excellent. The Hungry Cat is in my neighborhood and I go there all the time. There is excellent Italian at Angelini Osteria, on Beverly and also at it's sister restaurant La Terza on 3rd St. I can give you a dozen great Mexican holes in the wall or taco stands if that's what you're after.

I forgot about Angelini. We never go to LA without eating there at least once. It is fantastic.

Check out Campanile on La Brea Avenue. All the restaurants posted above are all excellent recommendations.

The place next to the library that LD referenced is called Cafe Pinot. It's literally right behind your hotel. I recommend it out of pure convenience, but the food is excellent as well.

Some might find it interesting that for the very first time, Spago was named most popular eatery in Los Angeles in the 2008 Zagat.

I think all of the Patina group restaurants are superb. They also have free corkage, although I'm not sure you can really take advantage of that, being from out of town.

Having had countless meals at Cafe Pinot (default lunch choice for biglaw recruiting/summer associate lunches) I think the service can be uneven, and once in a while you get a poorly prepared meal.

I've never had a bad meal at Water Grill, though I've had some panic attacks when the bill arrives.

Still in downtown, Engine Co. No. 28 at 6th and Figueroa is usually quite good if you are in the mood for meat and potatoes type food.

I had nice dinner at Ortolan on 3rd a couple of months ago. The food was quite good and actress Jeri Ryan, who is married to the chef, was working front of the house that night--she still has the Seven of Nine body going.

Urasawa.

I'd like to add two of my favorite LA restaurants to the list: Grace and Sona.

for cheap:
+1 on Phillipes...sounds like your hotel is within 5 min drive (about 3 blocks north of Union Station)

Vito's pizza on La Brea/South of Fountain for great pizza slices. Good place to go if you're going to check out Beverly Center (Vito's is about 3-4 blocks north of it)

Kouraku on 2nd St in Little Tokyo (also very near your hotel) has imo the best Ramen in the area. (cash only)

Mid - Upper range:

I really like Gyu-Kaku which bills itself as "japanese BBQ" but it's really a Korean restaurant that the owners (smartly) market as "Japanese" which I think many diners find more accessible than korean cuisine. There is one on La Cienega iirc (I go to the one in Pasadena)

Chaya Brasserie on Alden/Robertson (right next to agnes b, kinda across from famous restaurant The Ivy) is one of my faves in LA

+1 on Shiro in S. Pasadena. It seems every table has an order of the catfish happening.

Koi if you want to eat where the celebs eat (also The Ivy during lunch)

There are some good restaurants on La Brea, but Vito's ain't one of them.
Maybe they need to have street signs in Chinese for you as well as English?