The ID
South of the downtown core, nestled next to the train station and a stone's throw from the baseball and football stadiums is a neighborhood called the International District, or "ID." This neighborhood is jam packed with Pan-Asian restaurants, stores and culture and shouldn't be missed on any tour of Seattle.
If you're interested in eating an authentic and delicious Asian meal, the ID is where it's at. Dim Sum, hand shaved noodles, soups, etc. all congregate in this 16-block square area. Currently, the best online resource dedicated to ferreting out the best places to eat is called MSG-150. The writers are eating at and reviewing every restaurant located within the ID. My personal favorite is the Jade Garden for Dim Sum (on 7th).
Yes, Uwajimaya is a grocery store. I still recommend visiting it because it is amazing. Not only does it have a vast selection of food, books, and just about everything, but included in that everything is a great selection of souveniers for the traveler. Uwajimaya is also practically a historic landmark, having been located in Seattle since just after World War II.
Culturally speaking, one of the highlights is the newly reopened Wing Luke Museum (a Smithsonian affiliate). Now located at 719 South King Street, the Wing Luke Museum celebrates the rich Asian Pacific heritage that is present in Seattle and the Pacific Northwest.