Speaking of restaurants we really liked the Crab Pot in Seattle down by the cruise terminal.
The Crab Pot is fun, but I always want to recommend a non-chain restaurant to eat at when it comes to Seattle. For the same price you can get food that is some of the best in the world.
I have a very proper older aunt who visited us and wanted to go to a seafood restaurant. We tried to tell her that you could go into any local establishment and get great fish, it didn't need to be seafood specific. She insisted--and she was being a bit of a pain that week anyway... so we took her to the Crab Pot. The look on her face when the food was dumbed on the table into a pile was priceless.
For those staying at the Edgewater Hotel, there is an amazing place called Local 360. Its a block down and three blocks over. Lots of foods kids will like (comfort food), but elevated dining for parents. All of the food comes from sources no more than 360 miles away, even the sodas. Try the PB&J BonBons. If mom and dad want a nice meal, but need something the kids will like, this is a great place. Also, amazing happy hour.
Also on 1st just north of the market is Ohana, for Hawaiian food and Spur Gastropub.
In the market is Japanese Gourmet, Steelhead Diner, Falafel King (best in Seattle), and many, many walk up stands. The food in the walk up stands will be better than any chain place you will ever go to.
If you're willing to walk another block or two, go to 2nd Ave to Pinxto (my favorite Spanish tapas in town, happy hour and dinner only), Mama's Mexican Kitchen (a locals favorite), Cafe Casbah (counter service sandwiches, great espresso), and for those 21 or older--the great Seattle institution of Shorty's (pinball and booze). A little further down is the Marrakesh (traditional Moroccan dining, local favorite for birthday parties, dinner reservations only).
I'm trying to decide if I should share my favorite hole in the wall oyster bar or not.
For coffee, take a picture at Starbucks, but go to a place like Local Color which is less than a block away. The coffee is better, and the people who own it are great. For tea, go to The Crumpet Shop, also in the market, also a great family who own and run it.
I also keep meaning to make a couple of recommendations for kids who are picky eaters. If they like hot pockets, see if you can get them to have Piroshkys (available at Piroshky! Piroshky!) or Humbow (at Mee Sum Pastry). Both are available in the market at walk up stands on the main drag through the market.