Good suggestions above, also in town the Anchorage Museum is well worthwhile especially on a rainy day, and the Flattop Mountain Shuttle can give you a few hours well above the city with beautiful views, hiking in Chugach State Park as little or as much as you can or would like. More information at Flattop Mountain, Hike Anchorage, Alaska with Flattop Mountain Shuttle.

The public bus system is extensive enough, especially this year when rental cars are very expensive, more information at https://www.muni.org/Departments/tra...sandstops.aspx

There is also an hourly shuttle this summer to Girdwood and other locations down Turnagain Arm, but I don't have any personal experience with the services provided. https://www.turnagainshuttle.com/