Peter...Yes, it should be relatively easy to find a berth for a few nights. If you are truly interested in being within city limits, I'd suggest South Beach Marina
). They are located more-or-less under the Bay Bridge, on the Embarcadero. Walking distance or a short cab ride, from pretty much everything the city has to offer, good and bad.
If you have a dinghy
(if you're cruising, I assume you do), you can anchor-out in Richardson Bay, off the town of Sausalito (spanish for "artsy-fartsy") . Plenty to do here for a few days, and not a bad cab ride across the Golden Gate bridge into San Francisco
There are several other options, but they take you farther and farther from the city.