You can easily find a studio for that price on Capitol Hill. A lot of places don't advertise, especially the cheap places. Just walk around Bellevue Ave E between Denny and Roy and then go up to Summit, or Harvard, making a loop around that area. Also, places past 15th ave are pretty cheap. The Stranger classifieds also have places for rent listed as well...
Georgetown may be *ok*, but you can only walk around that area, you can't walk to the downtown area, bus service is pretty bad, and you'd have to taxi anywhere else. Sorry, but that is lame. Also, it is already getting trendy (no need to wait 10 years, try 2 years).
All in all, I'd suggest another trip out here (if you can afford it) and write down numbers for apartments that have signs up. It'll be worth it. Capitol Hill is the most accessible neighborhood in the city, hands down.