Museums
Portland Art MuseumOregon Museum of Science and Industry
Oregon Historical Society
Museum of Contemporary Craft
Oregon Maritime Museum
Portland Children's Museum
World Forestry Center
Oregon Jewish Museum
The Hat Museum
The Velveteria (sadly closed, but nonetheless noteworthy)
Galleries
Portland Art Dealer's Association Frankly, there are so many that I'm simply going to provide a link to Portland Galleries. However, I will point out a few of my favorites:
Blue Sky
White Box
Butters Gallery
Launch Pad Gallery
P:ear
Augen Gallery
Blackfish
Disjecta Interdisciplinary Art Center
Artichoke Gallery
Film & Photography
NW Documentary Northwest Film Center
Portland International Film Festival
Hollywood Theater
Newspace Center for Photography
Artists Miscellany
Pacific Northwest College of ArtThe Portland Institute of Contemporary Art, otherwise known as PICA
...and of course its Time Based Art Festival
YU Contemporary Art Center
Oregon College of Art and Craft
The 24 Hour Church of Elvis