I agree with all the above (though I haven't done everything). What we have done (or want to do in one case).
Chinatown - there are plenty of kitschy and touristy shops but it has a certain appeal and if you get beyond the touristy, you find plain diners that serve great Chinese food for not a lot of money. Some of the tourist shops had some nice items for not a lot of money. I was fascinated just watching fortune cookies be made at a place you entered off of an alley
Golden Gate National Recreation Area. The "Batteries" north of the Golden Gate Bridge have the iconic views of San Francisco.
Bay Bridge Lights -
http://thebaylights.org I'm using this as an excuse just to go to San Francisco. Depending on when you get back from Alcatraz, you could walk toward the bridge along the Embarcadero and just take in the views and shops. One of the ferries to Sausalito leaves from the ferry building and it has a market place and restaurants we have enjoyed. This isn't the typical mall experience.
http://www.ferrybuildingmarketplace.com
Of all the places we have stayed, I enjoyed staying around Union Square Park
http://unionsquarepark.us. The hotel costs were not bad at all compared to the touristy hotels along Fisherman's Wharf especially if you can get a good weekend rate. It is centrally located, on or close to the trolly lines, and within walking distance to pretty much everything.
To us, more so than almost any city, San Francisco is about just walking around an experiencing it. Within a matter of a few blocks you can go from high end shopping (Union Square) to the simple shops in China Town. There is even a gorgeous hotel bar/restaurant in or near the financial district supposedly frequented by Mark Twain. I had dinner there a while back but a local will have to direct you to it as I don't recall the exact location.
Take warm clothes. Even in summer. Especially in summer. (I mean, the ushers wear parkas at Giants' night games in July, the vendors sell out of warm nuts) But if you forget, there are plenty of sweatshirts in the tourist shops along fisherman's wharf (which is entirely touristy / watch out for "plants" that attack you).