We spent 3 days in Anchorage in 2015 at the end of visiting the Denali State and National parks, and had a very relaxing time and very much enjoyed it. What we did was very low cost and without a car.
Watched anglers fishing for salmon by the side of the river - plenty were caught.
Walked the town, which is well set up for pedestrians, visited the earthquake museum.
Rented bikes and rode a good portion of the bike trail around the waterfront. We turned back after 10 miles when we encountered a moose grazing right next to the trail.
Took a walking trip out to Flattop mountain, with a tour company at one of the shops on the street. There were about 15 of us on the trip, mini-bus out to the mountain and back again after we had been left to do our own thing. ( we made it to the top
)
Flattop Mountain - Hike Flattop Mountain Rocky Mountain National Park