Chain Reaction in South Anchorage is a good shop. REI has or had some great bike maps of the area. There are a lot of multipurpose trails. The best known is the Coastal Trail but they criss cross the entire city. Not much in the way of bike specific trails...and really poor road riding as most of the major streets are very bike unfriendly. Do watch for moose and bear here and there. You'll be lucky to see a bear but moose can be a real concern, particularly cows.