The four mainstream hotels closest to Century Link Field are the Silver Cloud - Stadium (#32 TripAdvisor), Best Western Plus Pioneer Square (#27 TripAdvisor), Courtyard Seattle Downtown/Pioneer Square, and Arctic Club Doubletree (#15 TripAdvisor).
The Silver Cloud is closest to the stadium. In that sense it is also most isolated from the rest of town but you said you are not really planning on much other than the game and they do have a local shuttle if needed. It would be a quick walk from the hotel's location on 1st Avenue S. right down Brougham to the light rail stop on 4th at Brougham or a reasonably easy cab to/from the airport.
The Best Western and Arctic Club are both walkable to the stadium though and are also convenient to light rail.
Hope that helps