Most people stay in the Fisherman's Wharf area, which is pretty central to Fisherman's Wharf, Chinatown, and North Beach (Italian area).
Another good place is the Union Square area, which is more central to the theater district, shopping, and financial district.
One of the cheaper areas to stay is out on Lombard street (neighborhood of Cow Hollow and beyond). That's where you'll find cheaper (note, not cheap) accomodations, mostly motels. Recommended if you're driving, as most of these motels do NOT charge for parking. Almost all other hotels/motels do charge for parking, and it can be high.
Lots and lots of things to see and do. Don't forget Golden Gate Park, with all its museums, outdoor displays of flowers, and the Conservatory. If you're driving, drive up to the top of Twin Peaks at night - the views are amazing! Also, when you go to the GG Bridge, go over it and immediately exit for the scenic overlook - great views of the city!
But for even better views, check out my post #7 and #8 in this thread:
http://www.disboards.com/showthread.php?t=2511788
-Bob