Was there on vacation a year and a half ago. I realize everyone has different tastes, but here are a list of my favorites...
USS Midway Tour...very cool. When standing on the deck of the ship, it is amazing how big the ship is. It is a self guided tour(mp3 players) except for when you go up in the bridge where volunteers take you up 10-15 at a time.
LaJolla...forget the ritzy shops and instead spend a half day wandering along the waterfront at LaJolla Cove. One of the favorite parts of my trip.
San Diego Zoo...Outstanding, especially if you get to see the Pandas while they are active. Happened to be there within a year of when the baby panda was born. Worth the price of admission. Wear comfortable shoes and take the bus tour to see the outer parts of the zoo.
Harbor cruise...take the one that goes both North and South of the city.
Point Loma - Cabrillo National Monument. Fantastic views of the city, harbor and Pacific Ocean. Worth the drive. If you are going to see this, go on a clear day! There is also a military cemetary about halfway up the hill, that I wasn't even aware of. Truly moving to see all the white crosses.
Aerospace Museum...very nice museum dedicated more to aircraft than outerspace. You can easily get caught up in all the exhibits and end up there for a half day or more.
If I had to classify some of these as MUST SEE, they would be LaJolla Cove, Point Loma, USS Midway and the San Diego Zoo.
We also went to Sea World and Disneyland, but if you don't have kids, I'd skip them in favor of some of the places I've listed.
I don't have any recommendations for nightlife or fine dining as we had a 10 year old in tow.