In contrast to the above poster, honestly I think the timing of your trip is quite bad, especially considering you can't rent a car. There are some nice boat tours from Whittier that are still operating, but you can't get there easily. The train no longer operates and many shuttle services have stopped by then too. You might check with the operators in Whittier (26 Glaciers or Prince William Sound) to see if they offer transportation from Anchorage. That would be a great option for Sep 27th.

I would rather pay a bit more for a hotel and have options on sightseeing than pay a cheap rate for a hotel and have extremely limited touring options. No wonder the hotel prices drop!

I would try to rent a bicycle and bike part or all of the Tony Knowles Coastal Trail. Check Downtown Bicycle Rental or Pablo's Bike Rental.

You can see if the AK Public Lands Information Center, the Earthquake or Aurora films are still playing and check out the Anchorage Museum. You can take the public bus to within spitting distance of Lake Hood (near the airport) to watch floatplanes take off and land (or bike there from the Tony Knowles Trail). Check out the Aviation Museum near there too.