Hiltons will be tough in a good LA sightseeing location at that rate. Before I moved out here, I used to stay at the Doubletree in Westwood - it was a little bit of a dump, but great location for what I wanted. The Beverly Hilton is about as central as they come, and nice, but it will also be in the low $200s at best.

My typical suggestions for decent rate/central location/relatively nice hotel mix include the Crowne Plaza Beverly Hillls, The Ambrose in Santa Monica, and the Hyatt West Hollywood. As suggested, search the various LA threads as there are many many posts on the subject.