We just completed a week in San Diego, staying at San Pebbles in Solana Beach, approximately a 20 minute drive from the docks.
I'd recommend the San Digeo "trolley" tour as a good starting point, basically a motorized trolly car that runs a two hour loop through four main tourist areas. You can get on and off of it while they operate, basically 9am - 4pm in the winter and the guides will give you a general idea of the history and lay of the city. Old Towne is the recreation of the pueblo origins of the city and is good for a couple hours of poking around and lunch, Corrando Island is pretty to see, both of which are on the trolley tour.
The aircraft carrier Midway is a museum docked next to the cruise ships and is something you can easily spend a day on. We gave ourselves 4 hours and felt like we missed a lot. Also Balboa Park is the main central park area of the city and features 16 museums of various interests as well as the San Diego zoo and you can easily spend a couple of days there. I'm an ocean person myself so I tended to gravitate to the beach. La Jolla is a great place to spend at least half a day walking, talking in the beauty and shopping. I like to swim from La Jolla cove in the open ocean, but in February water temps are likely to be in the mid 50's so unless you are a cold water swimmer that might not be to many people's liking.
It's possible to get some warm and sunny days but in February it will likely be in the 50 or 60's.