I've stayed at the Green Tortoise (cnr of Columbus and Broadway - http://www.greentortoise.com/) a few times over the years. I stayed there the first time I went to SF based on the recommendation of my friend. I've stayed there heaps of times since, it's my fave place to stay when I go to SF!
It's really laid back, good price, well run, they have heaps of events every night, a pub crawl, trips to Yosemite, and really fun, interesting people. It's also situated near lots of bars and a few clubs which are in that area, so it's only a short walk home after a night out! And best of all (unlike other hostels) they are 24hr and there's no curfew!
In terms of other hostels, there are a few on Broadway that I've seen but haven't stayed at, so you could always go check out Green Tortoise then wander around to find a hostel you like. almost 8 years ago
This might not be the best answer as all I can say is: Don't go to the YHA in Sausalito unless you have a car. It is in the middle of nowhere. A really nice location but no partying at all and it takes a while to get to the city.
As for the Green Tortoise, even though I did not stay there, I went inside to have a look. And it seemed really nice, friendly staff, good location, free internet. What more do you want?
Book ahead though! almost 8 years ago