Pike Place market is a large covered market downtown that sells everything from fish and produce to clothes and tourist trinkets. The clam chowder there is excellent and highly reccomended. Be warned that the market can be very crowded and if you want to miss the crowds I am told you should go at around 2pm.
The original Starbucks is in Pike Place. Although when I visited on Thanksgiving weekend it was packed and I did not get to go in. They did have a group singing outside though and according to others they have someone performing there all the time.