You can check out the nightlife on Sunset; it's a bit overdone for the locals, but it's fun for a visitor. Great people watching, you can check out the finsihed work of all of Beverly Hills' plastic surgeons!

Sunset is a great road to cruise--Keep going west, go through Beverly Hills, and it will take you all the way to the beach and Malibu.
You can even have lunch on Sunset, and the next time you see a move/tv show you will recognize the area. There's both fine dining, and even super-cool/budget (Try Carney's, it's inside a train car)
If you want to walk around Beverly Hills, check out Rodeo Drive, there's even free valet parking below the Two Rodeo center. It's on the corner of Wilshire and Rodeo, right across from the Beverly Regent Hotel--That was the hotel from the flick, Pretty Woman.
If you want to take it down a notch, hit up Pink's Hot Dogs on Melrose. It's a LA landmark. There's a long line there for a reason!
If you want a cool look at a movie studio, Warner Brothers has a VIP tour which is very informative (Not like an amusement park, such as Universal Studios).