Looking for a hostel to stay at in SanFran where I won't be horribly beaten.

Well hello.

I'm coming over to the US for a short period after living the vast majority of my life in what's essentially a large country town, so I am somewhat paranoid about what sort of neighbourhood I should look for accommodation in. (I'm a lone female traveller with overprotective upbringing and lots of exposure to mafia films.)

I don't have much money, so I was hoping to find a cheap backpacker's hostel or what have you in a safe part of the city. Having no knowledge of what the local neighbourhoods are like, I thought I would ask you wonderful people for advice. What's a good, cheap place to stay in your beautiful city?