In LA (vs. San Diego) is Olvera Street which is kinda popular.
http://www.olvera-street.com/
Similar to that (and Fisherman's Wharf in San Fran). is San Pedro
http://cityguides.local.yahoo.com/?loca ... n_state=CA
Both can be difficult to get to in traffic. Of course, if you've been to CA Adventure, you've sort of already seen a cleaner, fancier version of these areas! Similarly, there are lots of good malls, but Downtown Disney is sort of better and newer than most.
There are
great museums in the area, notably the Getty, LA County, Huntington, Norton Simon, which also has nice gardens to wander around.
http://www.losangeles.com/attractions/museums.shtml
And, of course, there are the beaches. Anywhere near a pier will have some shops and easier parking. Huntington is OK, I liked Newport Beach Pier area (fun restaurants like Spaghetti Factory and Crab shack are there) and Coronado too.
Have fun! 8)
And for the best sandwiches on the entire planet, after which you will weep to never have one again:
http://www.mariosdeli.com/
No, no... He's got a point.