A good way to spend sometime in Seward is at the Alaskan Sea Life Center.
http://www.alaskasealife.org/ Seward is a small town. On foot, i didn't see many places to shop, so i am thinking you might want to stock up in Anchorage.
Anyone looking for a way to spend a day in Seward might want to check out Kenai Fjords Tours. i've gone on a couple full day tours with them and been very pleased.
Happy Travels! ~ Splish