For your particular destinations, either one of the hotels at Universal or something in Hollywood would be a good spot to stay. If you're going with Hollywood, the Loews Hollywood Hotel is probably the best option. It's right in the Hollywood & Highland shopping center, which includes the Dolby Theater. It's right near the Chinese Theater and many of the other landmarks.
I stayed at the Godfrey Hotel Hollywood last November. It's a couple of blocks away from the big tourist attractions, but it's a great hotel, too.