I would recommend checking out the many options that exist in the way of the rent-controlled housing for low-income residents. With your income you may qualify.

A common rule of thumb is to spend a quarter of your income on housing, so living on the cheap side puts you at about $600-$700 per month.

Market conditions seem good right now for renters, with relatively stagnant or lowered prices (I just moved out of a 1 bedroom on Capitol Hill after living there almost 2 years, and they raised the advertised rent $25) and lots of places offering one month free rent and other perks.

As far as overall safety, almost all of Seattle is safe. Belltown gets a bad rap, but it strikes me as more of a sketch/crazy/transient factor than genuine lack of safety. The Central District also gets a bad rap for gang activity.

Belltown: expensive for the masses, see above re: safety. Lots of low-income housing here if you qualify, though.

Capitol Hill, Queen Anne, or Fremont: max out your city living cred. You could affordably rent a room in these neighborhoods, or studios can also be found here for $700. Amazingly, I'm seeing some one bedrooms below $700 on Capitol Hill right now. For a better-quality place (larger, more recent construction), think north Seattle.

Wedgwood, Ravenna, Phinney, Wallingford, Greenwood, Green Lake: this seems like your sweet spot, unless you are really set on a walkable city life in which case I strongly recommend you go for a cheap Cap Hill studio/1br.

West Seattle: similar to north Seattle neighborhoods above, but more isolated from the rest of the city. Safety level and rent are going to drop as you move south towards White Center / Burien.

Lake City, Northgate, Central District, Rainier Valley: very affordable, but among some of the less safe neighborhoods.

Personally, I like Capitol Hill, but how do you define cheap? Pretty much anywhere in Seattle is safe, but the only really cheap places are out in the burbs.

Areas to AVOID for sure: University District and Belltown - I've either lived and/or worked in these two areas and I'm not fond of either. It seems like people get beaten up somewhat frequently, although this being Seattle it's much less frequent than a lot of other cities. I think it's a combo of street dealing and frat boys.

There has been a recent rise in gay-bashing in the Capitol Hill area, but I think it's pretty rare still. Also I think as a general safety issue it's better to take a cab than walk around by yourself late at night right after the bars close - that seems to be the time when people have gotten beat up.

Hopefully others will give you their input - my main concern is the dudes who drive by slowly then offer me rides when I'm walking around at night by myself.

Crown Hill and Northgate are relatively cheap and safe, but pretty boring.

You can have safe, or you can have cheap.

You can't have both.

Sorry; it has been like that for some time now.