Get tickets to watch a game at Sullivan Arena. If there's nothing happening while you're in the area, you might like to check if they offer a guided tour of the grounds.
You'll find this notable sporting facility in the leafy neighborhood of Fairview. An admission fee applies, so make sure you factor that into your budget. But the sightseeing doesn't have to end at Sullivan Arena. Dimond Center, Anchorage 5th Avenue Mall and Anchorage Museum are nearby and worth a look.