These can be done in no particular order geographical or otherwise:
(a) Go to Pioneer Courthouse Square in downtown; ask a stranger where you can hear your echo.
(b) Visit the Portland Classical Chinese Gardens: http://www.portlandchinesegarden.org/
(c) Eat dim sum (visit Yelp, etc. to consider your choices). This will give you a chance to see Chinatown as well. There are tours of the underground passageways, etc. associated with the “shanghaing” of sailors.
(d) Visit the Rose Gardens/Hoyt Arboretum/World Forestry Center (these are all roughly in the same area of PDX).
(e) Visit OMSI: http://www.omsi.edu/
(f) Spend some time at the greatest bookstore on the planet – Powell’s: http://www.powells.com/
(g) Hang out in NW Portland; lots to do, food to eat, things to buy, etc. (though it has suffered from gentrification over the years). Many of the names of the characters from “The Simpsons” come from streets in NW. When I write “hang out,” what I really mean is walking 23rd, 21st, etc. and getting a feel for the place; it still has a wonderful vibe to it. Catch a movie at the artsy “Cinema 21” – a favorite old haunt of mine. Lots of night life here.
(h) Visit the Baghdad Theater and Pub (part of the “McMenamins Empire” as I call it): http://www.mcmenamins.com/219-bagdad-theater-pub-home
(i) Voodoo Doughnuts! http://voodoodoughnut.com/index.php
(j) Visit Waterfront Park.
(k) Pittock Mansion – where you will not only see a beautiful home from the early 20th century (with all that entails), but great views of the city (great views of the city can also be found at the Rose Gardens). The Pittocks were instrumental in the foundation of Portland. http://pittockmansion.org/
(l) During the summer there is “Trek in the Park” – where performers stage episodes of the original series in the park.
(m) Portland Art Museum, which has a great permanent collection (particularly of objects related to the native peoples of the NW).
(n) Drink from a Benson Bubbler (one of the many water fountains in downtown PDX – they were put in place the temperance movement in the early 1900s as a means to cut down on the drinking of alcohol – it obviously didn’t work).
(o) The numerous and beautiful public fountains of PDX: http://www.portlandonline.com/water/index.cfm?c=42348
(p) The Oregon Zoo (during the summer they have a concert series there): http://www.oregonzoo.org/
(q) Portland Saturday Market – really a must see: http://www.portlandsaturdaymarket.com/
(r) Go bowling: http://www.thegrandcentralbowl.com/grand_central
(s) Eat at the Wildwood (possibly the coolest farm to table restaurant I know of): http://wildwoodrestaurant.com/