If you have a car, a drive down the Seward Highway could be a good idea. Several places along the way to pull off and take pictures and take in the scenery, plus you could go down to the Alyeska resort and take the tram, or a little further to the Wildlife Conservation Center or Portage Glacier (about an hour from downtown Anchorage)
The Native Heritage Center someone earlier recommended is great too.
Obviously there are plenty of spots for hiking if you wanted to do something more active.
If the timing works, the sunsets in Anchorage are incredible. We w