No Marriott at the airport. The only true Marriott is downtown, though other Marriott brands are scattered around the city.
In increasing distance from the airport:
- Courtyard at Int'l Airport and Spenard
- Fairfield on C St at Tudor
- SpringHill Suites on C at 36th
- Downtown Marriott on 7th at I
- SpringHill Suites University Lake by UAA/APU
Really, Anchorage is a small enough city that the difference in time between the Courtyard and the Marriott downtown is 10-15 minutes. All but the downtown Marriott have airport shuttles, too, even the SpringHill Suites University Lake (last I checked).