Hi Ann! I would agree with staying in San Fran and taking public transpiration to Oakland. Lodging can be expensive in San Francisco and deals are hard to come by. All our recommendations are on our AT&T Chasers Guide page here. I went about 10 years ago and took the ferry from San Fran to Oakland. It was fun but then you still have to take a cab to the ballpark. It would be pricey and probably not the best option for a large group including kids. Have fun!
We are going in late July. Three of us - two adults, one teenager. We are staying in Berkeley instead of in SF proper. SF hotel rates are very high, and we found it cheaper to stay in Berkeley at the Doubletree with a rental car than to stay in SF without a car. Our plan is to spend a couple of days in SF and we'll take the BART train to/from, and I'll do one game in Oakland and just pay to park. If you do stay in SF, the city is amazing, with lots of areas to explore and pretty good transit. Enjoy your trip!
I saw that there is a $5 deal when we there. I planned to look in to that.
With that many people you may be better off doing an Air BnB.
SF (and Peninsula) hotels are going to be $$$$. Or you will be staying somewhere you don't want to be. So staying in Oakland/Berkeley may be a better bet from a $$ perspective.
Mass transit works great in SF, though you may still use taxis, a bit.
Weather will be warmer in Oakland (even on the same day).
And if you sit in the outfield at ATT, the tickets will actually cost you an extra $50 because you will spend that on a sweatshirt since you won't bring the proper clothes. (Try to sit between the bases, if you can, for warmth. And third base side is the sunny side at ATT - too much sun for my tastes) First base side beyond the infield is nice at ATT. Even in the third deck. Much better views from up high on first base side than on third base side)
But, yes, easy to take BART from SF to Oakland for a game.
Ann -- I did that same trip with my two kids a couple summers ago. We also use Priceline and ended up at Fishersman Warf. Very touristy, but it was the best deal. We took public transport to and from both parks -- day game in Oakland, night game at AT&T. We were there in August and it is impossible to explain how cold it was at AT&T. As Al said, you can't seem to dress warmly enough. We brought a spare blanket from the hotel to wrap up in. It was a great trip. Y'all have fun.