Real estate prices are murderous all throughout the Seattle area. Lake Forest Park is a decent place to live, and it's possible to commute by bus from there to UW . See
http://transit.metrokc.gov/ for general bus info ... as a UW student you will be able to get a very cheap, possibly free, bus pass.
If you have the inclination, you can quite reasonably commute by bicycle (!) to UW from there (google for "Burke-Gilman Trail" to see the route; the Wikipedia entry for it is useful too).
I used to be UW faculty, and my offhand assessment is that for a daily commute to UW I wouldn't want to live any further north than Shoreline - Lake Forest Park - Kenmore and any further south than First Hill. I am, however, a road rage kind of guy and I hate driving in traffic. I know people who live
much further away than that.