Hostels(as apposed to Hotels or Motels) are the most economical places to stay ,and they are safe to stay at,as they have lockers in which you can store your luggage.You can choose from staying in a bunk type room with others or pay more and have your own room.Hostels are within the $20-40 a night range.There usually is a community TV to watch and a small restaurant within the hostel.Most hostels are located in the inner city close to the heartbeat of the city.Now you will have money to see the sights,like the wharf,Chinatown,Coit Tower,and riding the streetcars.

Have a good look around Fisherman's Wharf

Muir Woods, Sausalito, The Wine Country and Fisherman's Wharf..take a ride on a trolley car..eat chocolate at Ghiardelli's, and Alcatraz...Muir Woods, Sausalito and the Wine Country are outside of San Francisco possibly a day trip..but well worth it.

Depends on your interests...I liked Coit Tower, Chinatown, including dim sum and shopping (I got some of those little white and blue china bowls for rice or soup like 4 for a dollar) never made it to Alcatraz but I wanted to go, Golden Gate bridge - very photogenic, art galleries across the bridge in Sausalito, lots of time in Golden Gate Park exploring the different plants - I'm an avid gardener - and then finding myself at beachside, several visits to sfMuseum o Modern Art (sfmoma) (I like art), sfso-sf symphony with cheap student seats.... I had a car a couple of times, and enjoyed driving on that hill that's the most crooked street - can't think of the name, the hippy district was pretty cool (haight-ashbury) and very walkable; as was the glbt district (the castro), but ultimately city life was too urban for me, and I did enjoy my escapes to the N side of the ocean with whale and seal and doplhin watching, especially near Point Reyes and Bolinas and Bodega Bay (and the bakery's cinnamon buns there are the best ever) and the redwoods too. I think wine country is fun, with a friend, which you may want to try and make if you are traveling alone, beforehand, maybe via online means. Also, my ex had a visiting student thing at stanford, so we went to the bay area like 3 times a year, and I was free for the day to travel around, so I usually stayed in the s of sf area the first night as we got settled in, and checked out palo alto, and san jose (which is 'silicon valley'), and sometimes friends in oakland, 'across the bay' and would meet up with us, or we would go there and check out the UC Berkeley area. Ahh, the memories.... As for cheap...BART, bay area rapid transit - a combo of subway and buses - check it out...I bart'ed from the airport when I've not had a car, rather than taxi-ing it; You could get around the west via green tortoise, which also has it's own hostel in sf, and one in seattle: http://www.greentortoise.com/ and trips out from sf...I've never done it yet, but have always wanted to. I did stay at the following hostel, when I was a student attending a Flash conference: Hostelling International-San Francisco City Center‎ - and there are many others too. Just stay out of the "Tenderloin" area at night...not very safe. My hostel stay was cool...I had a roommate from Venezuela, (bunkbeds) and talked with several guys into the night, including one guy from Amsterdam who ran his own 'coffee shop', and another guy, a professor from NY, and a couple of guys from S. Africa. SF is a foodie city so try some new and different things! Have fun...bon voyage!

I totally agree with the suggestions given by the other answers (especially the Ghirardelli's!). The one thing I would add would be a side trip to Monterey and Big Sur. The scenery along Highway 1 is breathtaking.