Well you have limited time, so you'll have to pick and choose. You mentioned the Museum of TV and I happen to be a huge fan of classic tv and radio and love the museum in Beverly Hills. It is in a gorgeous building with huge windows that overlook Beverly Dr. in downtown Beverly Hills and you can combine a visit (2 hours minimum I would recommend) along with a meal and shopping or strolling in Beverly Hills. However, I wouldn't consider the museum a must see unless you're not planning to visit the one in New York City and are a huge fan of classic tv and radio like I am.
If you're interested in Hollywood, you could check out the footprints in front of Grauman's as well as the stars names on Hollywood Blvd. That's very popular for a lot of people. A drive down Mulholland is nice but it may take up too much of your time--unless you combine it with Hollywood sightseeing as the start of Mulholland is near Hollywood. Santa Monica and Venice are nice places to (especially if you like people watching) and a beach atmosphere.
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