Sorry, did not read through the whole thread so these may already be suggested.
I'm a nearby resident, which is both good and not so good (never been a tourist there).
Golden Gate Bridge walk, a must. Stunning to be able to see both the Pacific then turn to see the SF Bay.
Go to North Beach (Grant and Green, around there) and walk around during the day. Not a real tourist spot (say like Pier 39 or Fisherman's Wharf), just a vibrant part of town during the weekend.
Go to Lands End (near Ocean Beach). This is a trail at the westernmost part of SF. You get to walk on a nature trail that lets you look out on the Pacific Ocean without any development around. Amazing in a city the size of SF.
Walk along the Embarcadero. You can walk from Pac Bell Park all the way to Pier 39. (Google Map 1 Market Street, which is the Northernmost foot of the City) Amazing to walk along the waterfront with interior vistas of the Bay.
Have fun.