Museums
A Wealth of Museums.
Downtown:
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Portland Art Museum
Downtown Park Blocks & Jefferson.
Oregon History Center
Downtown Park Blocks & Jefferson.
Oregon Sports Hall Of Fame Museum
Oregon Maritime Museum
On the waterfront
Oregon Jewish Museum
Downtown/Old Town.
Oregon Nikkei Legacy Center
Downtown/Old Town.
Mercy Corps
Downtown/Old Town.
Multnomah County Central Library
Full of books, beautifully remodeled in 1997 and free. 
Velveteria
A Museum of paintings on velvet. Yes. Really.
3D Center
Art and Photography
Close in Southeast Portland
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Oregon Rail Heritage Center
Oregon Museum of Science and Industry
(OMSI)
On the river near Hawthorne Bridge. Look for the submarine. The Hat Museum
located in "Ladd's Edition" (close in).
Southwest Hills (all at the same bus stop):
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Oregon Zoo
World Forestry Center
A great interactive museum for kids from 4 to 100 that teaches about the value of forests around the world.
Vietnam Veterans Memorial
See also
Children's Museum
Portland Children's Museum is the sixth oldest children's museum in the world and the oldest West of the Mississippi. The 50,000 sq. ft. Museum receives over a quarter of a million visits from children and their families every year.
Northwest Hills:
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Pittock Mansion
One of America's Castle homes.
Aviation & Space:
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Evergreen Air Museum
Spruce Goose, SR-71, Warbirds, Rockets. 1-Hour from Downtown.
Tillamook Air Museum
90 minute drive, on Oregon Coast.
Pearson Air Museum
Vancouver Washington.
Western Antique Aeroplane & Automobile Museum
Hood River - 1 hour East on Hwy 84
The Museum of Flight
Seattle at Boeing Field. 4-hour Drive.
Flying Heritage Collection
Everett WA. A private collection not a formal museum. 5-6 hour drive.
1 hour or less from Downtown Portland:
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End of the Oregon Trail Interpretive Center
Oregon City
Washington County Historical Society & Museum
Beaverton. In the "Silicon Rain Forrest." Exhibits include the original Washington County Jail built in 1853.
Pacific Northwest Truck Museum
Salem.
Tractor Museum
Antique Powerland Museum
Asahel Bush House Museum
Salem.
Marion County Historical Society - MCHS
Salem
Mission Mill Museum
Preserved and presents a Mission house, an Oregon Trail settler's house, a historic church and the structures, equipment, and original water-powered turbine of the Thomas Kay Woolen Mill with related artifacts.
Historic Deepwood Estate
Salem.
2 hours or less from Downtown Portland:
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Maryhill Museum
Columbia Gorge - 2 hours EastThe Maryhill Winery
& event venue, is nearby.The Stonehenge Replica
also nearby in Maryhill WA.