There is no legal camping near the city. If you have wheels, there are some campgrounds 10 to 20 miles outside the city center. If you have a boat, kayak, etc., you can camp on Government Island near PDX airport.A hostel membership and a 30 day stay would cost about $700 at http://www.nwportlandhostel.com/ a very nice location��though parking is a problem there. The one on Hawthorne Blvd., is about the same but different: http://www.hihostels.com/dba/hostels-HI-��The most obvious short-term alternative would be to look for a short term roommate situation in craigslist http://portland.craigslist.org/roo/ I see prices now ranging $300 to $675.
You can get a room for rent at a downtown hotel for $120 a week. Actually, it s been a long time since I have been there so I don t know how much. Look on Craigslist.org. Or, you can go to Portland and join a gym so you can work out and shower every day, and then find some out of the way place to camp.
You should look for a house rental. There are lot of choices for rentals in the WA area. It s best to do your homework and use online research to find available places to stay that fit within your budget.Rather than give you a specific property name and location, I would suggest that you do some research on the available houses/condos, the prices and the locations. I have used justvr.com in the past and it was quite helpful for narrowing down my choices and booking a few nights stay.
The best way is to sublet for a month from Craigslist. I did it once in exchange for cat-sitting. There are others like that. You can try Extended Stay America for a month or the Homestead Suites. That hotel for $120 downtown Portland is not very nice.
You can always be a bum on the street! Thats pretty cheap!