You can't go wrong just browsing and eating through Pike. Here are some good places off the top of my head:
Beecher's Handmade Cheese - you can watch them make the cheese and get a grilled cheese to go.
Piroshky-Piroshky - really good baked goods.
I really love the fresh crumpets from the Crumpet Shop. But it looks like it's under renovation and won't re-open for a while.
If possible, take a food tour. Either one offered at the market or from Savor Seattle. We took 2 tours from Savor Seattle last time and loved them both. You get to sample a lot of food from different places as well as some facts and history of Seattle.
Also, we had a few meals at BOKA Kitchen at the Hotel 1000 (just a few blocks from Pike). The happy hour deals are really good ($3 for truffle fries!) and the food was tasty. We've also had some wonderful desserts from there as well as a great breakfast.
Grand Central Cafe is a good place to grab breakfast or lunch. The bacon egg bolo is delicious. I also had a wonderful beet soup there.
For something sweet, I love the Chocolate Box. You can get a variety of hot and cold chocolate drinks. There are also lots of other chocolate treats to choose from.