A fun spot for riding right in Anchorage. Keep an eye out for moose!
Kincaid Park is a 1500 acre park in Anchorage that offers 25 miles of singletrack and a variety of trails. I'd recommend starting at the Raspberry trailhead to complete a big loop of the park. The trails are mostly super flowy, without any serious elevation gain. All-in-all a great place to ride for all levels of riders near Anchorage.
You can also access Kincaid by riding right from downtown on the Coastal Trail.
You can get a full trail map here (be sure to check which direction the trails are going while you're there, they switch between clockwise and counter clockwise):