I just looked this up. I did say I would be asking all day if people had turned their ballots in, so I thought I had better be able to tell them where they could do so.
Every single branch of the Multnomah County library system has a drop-box inside the library. The Midland and Gresham branches have drop-boxes outside. Every single branch of the library is routinely open until 8:00 PM on Tuesdays - some of them open at 10:00 AM and some of them open at noon.
There are other locations as well. Details over the orange decorative object.
Multnomah County Elections Office
SE Belmont between 10th & 11th Avenues
The site I checked says on the north side of Belmont across from the Elections Office. I used to live in the neighborhood, and I drive through there moderately often - they have generally been on the east side of 11th, to make it easy to access from the driver side of the car.
Pioneer Courthouse Square
700 block of SW Broadway
next to Starbucks, across from Nordstrom
Goodwill Store
3134 N Lombard Street
at north end of one-way lane
Regal Cinemas Movie Theater/M&M Car Wash
16603 SE Division
in the theater parking lot behind the car wash
A-Boy Supply
7365 SW Barbur Boulevard
at southwest corner of parking lot - enter off Terwilliger Boulevard