I used to live in Anchorage. There are two awesome sets of single track in the city. One at Kincaid park and one near the ski area Hilltop. They are put maintained by the Single Track Advocates association (Known as the STA trails). Either Speedway bikes or Chainreaction Cycles will be able to help you find them.
Chainreaction puts on the Abominable Snowbike Series (
http://www.chainreactioncycles.us) look at their site for maps that will have lots of good trails.
Feel free to PM me if you have any other questions.