I've held off on writing this hotel section for ages -- the thing is, I live here, why would I know about the hotels? But I can suggest looking into a few places:

The San Remo Hotel, over on the Wharf side of North Beach: (link). My sister used to like staying at this place. The rooms are small, but the atmosphere is good ("charming", as opposed to slick). Moderately-priced, but remember: shared-bathrooms.

Another thought would be the "Phoenix Hotel" (link), which is the place a band on tour is most likely to stay. You may run into them by the pool. Last I was here (some years back) I thought the rooms were just basic hotel rooms, albiet kitsched-up slightly, but the statuary around the pool area was super-cool (too bad the mural looming over it all has gone away). This is located in a not-too-nasty part of the Tenderloin, with some passible restaurants right there on the corner, and it's only a block off of the Polk Street corridor.

My third thought, is the Adante (link) a few friends of mine stayed here a year ago, and if they had any problems with the place, they didn't mention them. This hotel has a net cafe downstairs: "The 24 fps Cafe". If the line for computers is too long, there's always the Internet Cafe at Taylor and O'Farrell. This is definitely in the Tenderloin, but on the edge of SF's "Theater District", (which in turn is on the edge of Union Square). The less adventurous should probably make a point of entering and exiting from the east. Note: at O'Farrell and Mason is the cheap and yet excellent "Naan and Curry" restaurant, open 24 hours.

If you'd like something way cheap... I might suggest the Green Tortoise Hostel (link). If I read them right, they've got some private rooms with double-beds starting at $65. They're located right in downtown North Beach (or rather, above it, on one of the steep sides of Telegraph Hill). Just a few blocks from Chinatown.

Another possibilty is "the Red Victorian" B&B (aka "the RedVic", not to be confused with the movie theater up the street): link. The rooms start at around $125, and most of them look like the bed room of a hippie teenage girl, but this is in the middle of the Upper Haight zone, which for all it's flaws, can not be confused with Union Square.

And I suppose if you'd like something more luxurious, and aren't too worried about price, my pick would be The Kabuki Hotel (link) in Japantown. As of this writing, the room rates start at $160 a night, but at least you get something for it (e.g. a one day pass at the Kabuki hot springs -- but check the sched to see if your gender is welcome that day) and the Japantown neighborhood definitely has it's virtues.

If you want to keep looking around, I suggest looking either for hostels (on the low end) or bed and breakfests (on the higher end). There is essentially no reason to consider staying in the big downtown hotels: even if you can spend the money on it, why would you want to hang around with people willing to spend it?