There are miles and miles of fast double track trails that go up down and all around. Nothing very technical but very fast ant fun. An interconnected maze but maps are available sometimes at the visitor center. Beachside below the bluffs of Kincaid. Anchorage is mountain biking heaven.
Powerline trail is a great rollercoaster ride - up, down, through streams.
I'm a road guy, but I like the fun terrain, and especially the great overlooks. My favourite is the one with the bench that overlooks Star's field and pond. I hope someday I can go there with her again. Forgive me Star. Sure it is paved, but it has nice views and can get you back to downtown if you are doing a big loop ride around Anchorage.