Do you mean Hollywood or do you mean Beverly Hills?
If you want to stay in Beverly HIlls there is a restaurant, approximately 3 months old, called Villa Blanca....right in the middle of Beverly HIlls on the corner of Brighton/Camden.
If you love a relaxed atmosphere in a beautiful setting with beautiful servers (seriously gorgeous) and a chef who knows how to prepare wonderful fish dishes this is a good spot.
There's lots of attitude with good food although inconsistent service. I've been twice, had the black cod with miso both times (excellent) , but had different types of service each time.
The Ivy on Robertson is a place to see and be seen. Forget the Ivy on the Shore, it's not as appealing and the food is not as good. If you're going to the Ivy on Robertson, eat outside. It's comfortable and intimate with a garden setting. Some people enjoy the people watching. They make me a turkey burger and wonderful raspberry pie. One of the best martinis in town.
Of course there's Spago...wonderful food, impeccable service with a very high energy lunch crowd.
The Blvd in the Beverly Wilshire has a new chef, and typically fabulous Four Seasons service.
The Farm of Beverly Hills is classic.
Villa Blanca is new and supposed to be gorgeous.
Tanzore is a nice Indian place.
Don't know if you mean Hollywood, which is a little further east or West Hollywood, which has more to choose from, IMO.