beaverton stereotyping is derived from reality
the city of beaverton is entirely designed around the automobile. i have ridden/commuted through it and yes its possible to ride a nice route free of traffic. The older parts of portland however, were designed at an earlier time w/out so many automobiles. The city is full of narrow streets and bike blvd's. so for commuting, i'd consider it ideal. you beavertonians do have us beat on the recreational cycling in washington county however. you are much closer to nicer riding than i am in SE. more people commute in portland than in beaverton. check out the numbers on the hawthorne bridge crossing.
so for the search for housing, st johns is cheap and a nice ride to town. there are some cool neighborhoods off of interstate (cesar chavez) as well as the alberta/mississippi corridors.
also check out areas south of 84 but north of burnside, theyre allright. 50th to 82nd. The area just east of mt tabor is cool too. cheap houses, probably cheap rent. foster/holgate to clinton is cheaper too. i'd start looking there. milwaukie is always an option, 1/2 hr to 45 minutes to PSU and really cheap rent. i think that milwaukie is going to start getting more expensive in the next few years.
there are also a lot of cheaper duplexes, apartments, and one bedrooms in the central eastside.( inside 28th)