From what I've seen most downtown hotels do charge for parking. You could probably find someplace to park and take the MAX in though.
You can get really good deals on Hotels.com, Orbits, etc. DH and I used Orbitz and got a room at the Nines for really cheap. You often don't get to see the name of the hotel, but you should be safe with any 4 star. The Nines is the only 5 star in Portland so you can figure out easily which one it is. It's uber trendy, but fun and right downtown.
If you don't care about being downtown the McMenamins are fun- Kennedy School is near some fun artsy neighborhoods.