Next to the airport
When I'm feeling like budgeting is important, I usually stay at the Coast International. Very convenient to the airport (the closest hotel) with free shuttle service, it is a good bargain, summer or winter.
The room are big, and there are lot's of them. The hotel's lay out is such that you can have quite a hike to get to your room and I have yet to find an elevator - something to think about if you have a lot of luggage. I don't stay here as often as I used to as it just seems to really be getting run down and dirty. Don't have much choice but to downgrade to 2 stars.
Has a modest restaurant and a small sport's bar. Can get food in both until 11:00PM. The bar has outdoor seating overlooking Lake Hood which is great on those long summer evenings.
Just remember that the hotel and the airport are a ways from downtown Anchorage. About a $15 cab ride. But for a quick turn, I'd recommend the Coast for the budget traveller.