Hmm. Much depends on the precise definition of "reasonable"; I think there are still a couple of city-subsidized residential hotels downtown for the "one step above homeless" demographic, but that's the entire extent of my knowledge, and I suspect that there are hoops one must jump through before getting into one of those.
It is probably well out of the friend-of-a-friend's range, but you might have a look at the Mark Spencer Hotel
downtown; that one I'm aware of because an actor/theater friend used to stay there when in town doing a show. The rate structure looks not too dissimilar to a Hampton or similar, but it looks remarkably reasonable for what's offered (and where it is), there are definite price breaks for weekly/monthly stays, and any hotel that offers a rate package including a Powell's gift certificate has to be worth at least a first glance.
There are also two or three cheap-looking
motels out my way in Beaverton that may fit your parameters; one's close to the Beaverton Transit Center on Canyon, west of US 217, and another is across from the old Cedar Hills Shopping Center next to a strip club (just SW of the rat's nest that is the intersection of 217 and 26, not
next door to the Beaverton Powell's). I've never set foot in the one on Canyon, and it's been probably 30-odd years since I've been in the one at Cedar Hills, which I think is still called the Lamplighter -- at that time, the building next door was a Denny's and our basement had flooded.