Call the OHSU social worker. They get rooms donated for patient use, through the local Cancer Society. Hotels with spare rooms, donate a room or two and the stay is free. We have stayed up to 2 nights in different hotels, some with indoor pools, some with free breakfasts. You have to take whatever they have, but they have all been nice and on the bus route, if you do not have a car.
My favorite is the Residence Inn by Marriott, 2115 SW River Parkway, phone 1-503-552-9500. It is a 12-minute walk to the OHSU clinic (or a one-stop ride on the Portland Streetcar). They have a free shuttle that will take you anywhere in a 5-mile radius, and they're in "Fareless Square," which means you can ride any bus, trolly or streetcar in downtown for free.
They also have a complimentary buffet breakfast. And they offer an OHSU patient rate, which seems to range between $100 and $120 a night. I like the fact that each room has a full kitchen and separate bedroom.
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