In general the residential neighborhoods in west side of the city are going to be "safer" but they will be further away from the main tourist attractions. If you want to be closer to the tourist traps, I'd recommend staying as close to the Embarcadero as possible. Stay away from Tenderloin, SoMa, Mission, Bayview, Hunter Point especially if you are not used to urban environments.
Right now it's open season on tourists for property crime in SF, so be careful and vigilant as long as you are here.