The housing market in central Portland is more expensive than Vancouver, WA; but it's not nearly as expensive as Seattle. SE Portland has some great small 1- or 2-bedroom houses that can quickly become homes, but it's not really cheap. There are a lot of good apartments and townhouses in Hillsboro/Beaverton, but that can be a little out of the way if you're working a downtown or Gresham job. There are a lot of pleasant little apartments and condos just west of I-5 in the northwest quadrant, especially along Everett and Davis. (the "Alphabet" district)
And if you want a yard, just get a place near Park or a really nice job. (AKA 9th) No lawn to mow.
There's a building (kind of X-shaped) near PSU that has 1-bedroom, 2-bedroom, and Studio apartments; my dad lived there for a couple years when I was in Middle School and I think they ran pretty cheap for a downtown apartment (around $400-$600 a month?)
I can't remember the name of the building, but if you want me to check it out for you, I'd be happy to.