You can buy a 3-day transit pass that'll get you all around town w/ ease if you study the routes and plan ahead. I lived in SF x 25 years w/o owning a car and did just fine riding my bike and taking MUNI wherever I needed to go. And, it's pretty walkable, steep hills notwithstanding.
Last time I stayed in town, I did at the Hayes Valley Inn, on Gough, a Euro kinda place w/ shared showers and heads, though each room has a sink. Elsewhere, hotel prices are high, so definitely start looking now, like the tourists who descend on SF in August - lots of Italians then - already are. Same for restaurants, but check out the Groupons and similar deal sites.
In addition to the Big 4 art museums (DeYoung, MOMA, Legion of Honor, Asian), a walk along the Embarcadero all the way up to the Wharf and on to Ft. Mason, the Marina and Ft. Point is a must, and yes, do walk across the GG Bridge, and on up to the Marin Headlands for some really fine views. Check out North Beach at night, and the eye candy at Justin Herman Plaza eating their weekday lunches outside. Stroll thru the Ferry Bldg., and maybe even take the ferry over to Sausalito or Tiburon and back. If the Giants are in town, that's a good time, too, but pricey. Walk around Cow Hollow and Pacific Hts. to see some really fine homes and views; same for Russian, Telegraph, and Potrero Hills, each of which has its own little neighborhood full of shops and cafes. And, take a daytime walk thru the Castro - but save SoMa for the dead of night!