Ooh, my favorite city! I am a constant tourist there (I live about an hour away.)
Here are a few recommendations…
The Japanese Gardensare gorgeous (even in winter), and very authentic (designed by a genuine Japanese guy!) If you are the type to be bored by plants, there is quite a bit of interesting variety in the gardens–rock gardens, strolling gardens, and interesting architecture. These gardens are big and sprawling and naturalistic. They are located on the outskirts of the city.
In comparison, the Chinese Gardenis located in Chinatown, right in the middle of Portland. It is tiny and compact and perfect–designed in conjunction with the famous garden town of Suzhou (also known as the Venice of China), many of the building materials were shipped all the way from China. I highly recommend a guided tour, given by enthusiastic and interesting volunteers, who can give you all sorts of interesting facts and details you would never guess just from looking yourself. The attention to detail is amazing. Then drink tea and eat strange Chinese sweets at the tea house in the garden.
If you go to the Chinese Garden, you can go to the nearby Old Town Pizzafor lunch, a cozy gourmet pizza place built in an renovated 19th century hotel. Comes complete with a ghost story. You can go for dessert at the infamous “Voodoo Donuts” a short walk/drive away. This tiny little shop is a cult favorite, and and sells donuts with somewhat uh, non-traditional flavors. (Chocolate rice crispies and peanut butter! Vanilla frosting and grape powder!)
Also nearby, just up Burnside from the Chinatown gate, is Powell’s Books, one of the biggest used book stores in the world, taking up a full city block. It is an icon in Portland, and although their used books are over-priced and the lines are long, it is still undeniably worth a visit. Probably one of the only bookstores in the world where you actually need a map to get around.
My family usually stops at the nearby Thai Peacock for dinner afterwards. Delicious Thai food (in a town which is packed with Thai restaurants) at good prices and conveniently located within walking distance of Powell’s. (Head down Burnside from the main entrance to Powell’s and turn at the record store whose name I cannot remember.)
I also like the Portland Art Museum–a nice building, an excellent collection of Asian art and sometimes some cool special exhibitions.
If you ever go back in the summer, the Rose Gardens are beautiful too. And I second the recommendation of the Saturday Market–very hip and happening place, and very lively!
Will let you know if I think of anything else. Enjoy your time in Oregon.