Take the bus across to the Ferry building in San Francisco. Then take a ferry to somewhere else. I would suggest Sausalito. Nice view of Alcatraz, the Golden Gate Bridge, and San Francisco itself from the Bay. There are a couple of nice places to eat there. You can then take a Golden Gate Transit bus back across the Golden Gate Bridge. If get off at the south end of the bridge there are some things to see there. From this point, you can take a San Francisco Muni bus toward Pier 39. From that point, you can either take the "F" line street car, which runs "heritage" streetcars from all over the world, including PCC cars from several US cities. This route follows the Embarcadero back to the Ferry Building and then down Market Street. Alternatively, you can take an electric trolley Muni Bus from the vicinity of Pier 39 that goes through Chinatown. Carry on past Chinatown, with or without stopping back to Market Street. There you can get on The "F" line street car, or the Muni Light Rail one level down, or BART two levels down. After these experiences, you can then find one of the cable car lines. If you have the time, you could take BART all the way out to Millbrae and come back on Caltrain. From the Caltrain station at 4th and King Streets, you can get within half a block of walking to the Muni light rail, electric trolley bus, or diesel bus. Muni has a web site that has route maps. Golden Gate transit schedules can also be found on line. In fact, I think all the transit agencies in the SF aera have schedule and fare information available on line.
I would not walk around in Oakland at all. I have been to BART's office there by way of BART and about a 2 block walk, and know several people that work there. That area is not bad, in the daytime, at least. However, the general consensus appears to be that Oakland has no real safe area. There is only dangerous and not so dangerous.