Not sure of your budget, but if at all possible I'd go on a flightseeing hop on a floatplane operating out of Lake Hood (world's biggest seaplane base, adjacent to ANC.) In late September, with the prospect of "termination dust" (early snow) on the Chugach peaks, the views from light planes around Anchorage/Cook Inlet can be nothing short of heart-stopping. IMO well worth busting a budget, but of course YMMV. Rust's is probably the biggest and one of the elder operators there - http://www.flyrusts.com/

If the AA counter at ANC isn't open when you get there (and IIRC it doesn't open all that early - they use AS staff) there is a luggage storage service in the south terminal where you can store your bags for a few dollars per.