For just 2 days my first point is University of WA bookstore - love the campus, the other one is the Seattle Center where the Science Pavilion and Space Needle. We moved to WA in 1962 - that was for the Seattle Worlds Fair, there was a Food Circus that served food from everywhere in the world. Each country had a restaurant and you could order something from each one then sit at a table in the center of the building. It was there I discovered Belgium Waffles and lasagna. It has been a long time since I have been to the Center so not sure if the Food Circus still exists or not. The Space Needle is fun - expensive, but fun. You made need reservations since it is summer.
There is also an area called Pioneer Square - a lot of good eating places and art galleries.