Ride Mt Diablo when you get the 34T on. You can get close on BART. 10 miles of climbing, great views, then a fantastic twisting descent. (New tires and tubes, and brake pads, recommended.)
I am not staying very far from the North Gate to Mt Diablo. I wouldn't need to take BART. I did a hike up there a couple of months ago. 2000 feet of drop and then gain in a little over 7 miles. I was pretty wiped out at the end, but it was a fun day.