Lots of really good suggestions here.
I would also suggest the Point Loma Seafood place as it is exceptionally fresh seafood. Or the Brigantine on Shelter Island, which is also where the Red Sails is as mentioned earlier.
The Midway Museum is very good so I hear.
La Jolla is a great beach, it's where many of the 'rich folk' live. Other beaches are fine, but La Jolla is slightly better. Coronado is a very close second and they have a camping area to the south.
I personally would not go to TJ either, there's simply too much crap going on around those parts and so much in San Diego to see anyway.
There is Discount Gun on Morena Blvd, which is not too far from downtown. It has an indoor range as well. Then there is Turner's, SoCal Gun, American Shooting Range (indoor), El Cajon Gun Exchange, Duncan's Guns (smithing too) and La Mesa Fine Guns. There used to be many more, but have long since dried up. Oh, and the San Diego Police Range is right down the freeway from downtown too. They don't sell, but you can shoot there for $10 a day. Buy ammo there too.
If you want to you can contact me direct for any other information that you think you will need. I have lived here most of my life, know it pretty well and wouldn't mind helping you out at all.