I would not reccomend going to Oakland. The East Bay has some very nice areas but Oakland is not one of them. The A's stadium is not in the nicest part of the town and it is certainly not a "must see" stadium in terms of aura, architecture, etc. It is worth the drive across both the Golden Gate and Bay Bridge if you are renting a car. A drive through Berkley is nice as is Walnut Creek. Both are on the east side of the bay. As far as San Fran, there are several things I would reccomend. One, head to Union Square and ride the cable car to the Fisherman's Wharf. There is world-class shopping in Union Square and the ride from there to the Wharf on the cable car is a lot of fun.
The wharf has a lot of things to do. Can sign up for bay cruises, alcatraz, many restaurants, shopping, etc. I would reccomend not taking the cable car back to Union Square when you finish with the wharf. Instead, walk or cab to the North Beach region (little Italy). There are great shops and even better restaurants. Between North Beach and Union Square is Chinatown and I fully recommend walking through here. Truly a great experience.
If you are going to be in town for a few days, I would also recommend Muir Woods, which is directly north of the Golden Gate bridge. Another cool place is Haight and Asbury which is located by Golden Gate park.
Obviously, wine country in Napa and Sonoma if you have the time. If you like wine, this is a must. Another great thing to do is boat to Angel Island and do some hiking. The views of San Francisco from the island are top notch.
Hope this helps a little
