I lived in Antioch for about ten years, and one of the best things about living in the Bay Area was that anything you could possibly want to do in the world was no more than a 5 hour drive away.
The
East Bay Regional Park District has has 65 parks and over 1100 mlies of trails, and all that in only Contra Costa and Alameda Counties!! My favorite parks and hiking areas were Black Diamond Mines, just south of Antioch/Pittsburg and Briones Park, near Martinez.
Point Reyes National Park is a beautiful coastal area is very much is your reach from Vacaville. My wife and I honeymooned at the Golden Hind B&B in Tomales. Wonderful place!!
How about that state parks at a couple of the most prominent landmarks in your view?
Mt. Diablo and
Mt. Tamalpias both have state parks with plenty of hiking.
Right there in Vacaville is the
Travis Air Museum, right on the air force base. If you like history at all, there is a lot there to see.
Take a short drive up Hwy 128 and you're in the middle of
Wine Country. Go to a tasting at a vinyard!
Lake Berryessa is almost just up the road from you as well. Take 505 north to Winters, get off the freeway, turn left, and follow the signs about another ten miles or so.
And all of this before even getting into The City!!! If I were planning to be down there soon,
this is something I would like to check out in San Francisco.
Go to a baseball game!! I hear good seats are easy to get right now for the Giants and the A's!
Have a great summer, and enjoy your stay in the Bay Area!