In Anchorage and within fifty miles are a number of things to see and do. The Anchorage Museum, Native Heritage Center, Aviation Museum, Botanical Garden, and Zoo are excellent way to spend a part of you day.
Within fifty miles the Musk ox, Reindeer farms and Iditarod Headquarters are attractions north of the city. Heading south you have Portage Glacier, the Wildlife Conservation Center and Alyeska ski resort.
If you want to climb a mountain, you can do that in Anchorage, Hike, rent a bike and check out the hundreds of miles of bike and walking paths around the city.
Anchorage.net has a great website with all the information you need.