I'm from San Diego and I miss my hometown every day!

There is so much to do.
I agree the Midway is great. Fairly close to the airport is also the zoo (maybe not a good idea if your short on time), Balboa Park (which has several museums - two art museums, a photography museum, a train museum, a science museum, an aerospace museum, and a natural history museum. There are also street performers, fountains, and sometimes organ concerts. Also, there is a theater that is a replica of the Old Globe, and some walking trails. It is probably my favorite spot in SD (the park's inspiration was modeled after Seville in Spain), and Old Town San Diego which has some great Mexican restaurants, an old school house, old court, shops, and an adobe from the 18th century.
As for your luggage, I don't have any recommendations since I've never had to try to store luggage there.
Keep in mind that traffic can be very, very bad so leave yourself plenty of time to get to the airport (although travel time between the airport and the attractions listed above should only be 10 to 15 minutes.) Whatever you choose to do, I'm sure you will have a wonderful afternoon.
Enjoy your time there!
