You're on one of the last ships of the year, then.
There's plenty of easy walking right in the downtown area. If you're an ambitious hiker and have a few hours with decent weather, get a cab to take you to the Deer Mountain trailhead above town.
I was actually in KTN this past weekend. Other than having to do some advance planning and funding to accommodate the Airport to Nowhere, it's a great place to spend a few days.