The neat thing about San Diego is that it has several very culturally unique neighborhoods that feature restaurants, museums, shopping, etc. that are distinctive to each.
As another poster mentioned, Old Town is a fabulous place to find authentic Mexican food (even though Tijuana is so close, getting there, and especially back, can be a pain if you drive and with all of the post-9/11 security measures). Ocean Beach (OB) is a very laid-back, eclectic place with a great vibe. It’s my favorite neighborhood (because it is so low-key, friendly and kinda hippy). Then you’ve got the trendier section that is the Gaslamp. It’s cool to walk through and there are a couple of good steak places, but be prepared to see lots of tourists.
There’s also Hillcrest, which is cool and fun and full of really nice (and cute) gay folks. Hillcrest has great restaurants, cafes, clubs…it’s my second favorite spot. Mission Beach has the roller coaster and beach that’s swamped on weekends. Still, can be a good place for a meal and a drink…Pacific Beach can be, too, though the crowd is definitely younger.
Since you’re moving there, it would be a wonderful opportunity to explore. The beaches are amazing, the climate is incredible, they have a football and baseball team (just got back from a Padres game and it was lots of inexpensive fun), hiking, kayaking and other outdoorsy things to do.
Some links to the San Diego Reader and Union Tribune: