I kinda like

1. Venice boardwalk, muscle beach, etc.

2. Melrose with the weird shops and culture

3. Beverly Hills Rodeo et al, of course

4. Museums? Of course. I love the MOCA Museum of Contemp Art downtown. The automotive museum across from LACMA (County Museum of Art). There is a cool miniatures museum there too and you can eat at Marie Callendars right there which is neat inside and the food is good.