Parking in downtown Portland
You don't have to pay $20-28/day for parking.
Parking on the street is free from 7 pm to 8 am.
The downtown lots usually have daily rates from $7- $10 which works from about 8 am - 7 pm (check with the lot). So if you don't mind moving your car around, you can park in downtown for about $10/day.
Paid street parking uses a ticket machine system (like Seattle). There is usually a ticket machine in the middle of the block. I believe it is $1.50/hr. The machine issues a sticker which is placed in the window nearest the sidewalk. The machine will post what the max time is for that block. I saw times ranging from 60 minutes to 3 hrs (along river).