Places we like and keep going back to:
Breakfast - Snow City Cafe is "the place to go". The food is really good too.
Lunch - Glacier Brewhouse
Dinner - Sacks Cafe and Orso
Things to do - The Anchorage Museum is a fascinating place. There's a permanent exhibit, "Alaska Native Culture",with many artifacts on loan from The Smithsonian that gives you an overview of the diverse Alaska Native Peoples. Also lots of other wonderful stuff. We make it a point to spend half a day there every time we go to ANC. Our last 2 trips were this past March and September 2013.
Downtown Anchorage is completely walkable