You don't mention what your interests are, so I'll list a few ideas for you. There is plenty to do in and around Stockton for a few days to keep you busy.
If you are into hockey, Stockton has a professional hockey team called the Stockton Thunder. They play in the downtown arena and draw a great crowd.
If you enjoy wine, I would suggest a trip to Lodi, just 20 minutes north of Stockton. I consider Lodi to be what Napa used to be like 30 years ago. The wineries are still vastly accessible with quite a variety to choose from.
If nature viewing is your thing, you must take a drive to one of the several wildlife refuges outside of town (Consumnes is one). Being the southern end of the Pacific flyway, you'll get a chance to see about a zillion birds (okay, that's an exaggeration). But it is quite amazing. Ordinarily, I would suggest a boat trip on the Delta, but December can be a bit cold and foggy. If you bundle up on a clear day, the best way to enjoy Stockton is via the water.
I agree with the previous posters about things to do in the foothills and around Gold Country. Columbia State Park is very nice. Jamestown, Angels Camp, and Sonora are all quite historic. Again, if you like wine, there are many foothill wineries to choose from.
For the arts, depending on when you're planning your December trip, Stockton Civic Theatre will be staging Cinderella. Stockton is also fortunate to host not one, but two productions of the Nutcracker, one by the Stockton Ballet Company and the other by the Capitol Ballet.
It's only 75 minutes to Walnut Creek and the outer Bay Area. Outside Walnut Creek is Mt. Diablo State Park, the highest mountain in the Coast Range. They say that from the top of Mt. Diablo on a very clear day you can see up to 200 miles. I've hiked up to the top, though you can also drive to the summit.
In Stockton, there are some very good restaurants to choose from.
Enjoy your trip to Stockton!