I'm a solo female traveler and I stayed in this area a few years ago. I stayed at the Travelodge Motel at Columbus and Bay Street, which is probably not what you are looking for, but across the street from the Travelodge is San Francisco Marriott.
The next street up, North Point Street, there is a Holiday Inn Express, a Hyatt Centic and then the next street up again , Beach Street there is a Courtyard By Marriott.
Take a look at the these hotels on the map, this area is where I would recommend, as its all walking distance to Pier 33 for Alcatraz and the main Fishermans Warf shopping and restaurant area.
I walked from Travelodge along Bay Street to Pier 33 which is Alacatraz Landing.
I would recommend getting your tickets for Alcatraz ASAP, as they sell out.