My suggestion would be to take a shuttle to one of the airport hotels, sit and relax in some comfortable chairs, and have something to eat or drink. My personal favorite for doing this is the Marriott because of their spacious lobby and picture window overlooking the bay and the airport.

In addition if you don't want to just sit, there is a path just outside the hotel that goes along the bay in both directions. It can be a very pleasant walk if the weather is OK, and if you have bags, you can just check them with the bellman.

Of course, you can also now take BART from the airport into the city. Then your possibilities are endless. Either the area around Union Square or the Embarcadero (Hyatt Regency) and the Ferry Building would probably be the most convenient and offer the most possibilities within your time frame.