Third Street Promenade for shopping and people-watching. Hiking down to the Santa Monica pier would make for a nice afternoon.
Or drive north on PCH 25 to 30 minutes and hang out on Zuma Beach in Malibu. Stop at Malibu Seafood on the way up and have fish & chips on the beach. If you wanna see some cool views drive the loop around the top of Pepperdine. I enjoyed it for 4 years.
Hit up
anywhere along here for cool pubs that draw tons of 20's and 30-something heads on Fridays and Saturdays.
You could take the 10 to the 405 N and drive up to the Getty Museum.
You can also make a short trip down to Venice and stroll the boardwalk.
What kinda things are you interested in, particularly?