The Sheraton has just opened but it is not the only chain hotel in the area. If you want IHG hotels, there is a Holiday Inn Express and a Crowne Plaza. Both are very close as well. You can take the tram from either terminal at the airport and be there in 5 minutes or so. The tram is free from the airport to this stop (Grand Arenas) and both the HI Express and Crowne Plaza are just across the road from the tram stop. If you arrive at terminal one, you could also walk there in 5 to 10 minutes. It would be too far to walk from Terminal 2 but, if you arrive from LHR, you will be on BA, which use Terminal 1.

There is a Radisson Park Inn in the vicinity of the airport as well but it is currently closed and expected to re-open in July so no good for you. There are also several Accor hotel properties (Ibis, Ibis Styles and Ibis budget) within close distance (viz.within walking distance of the terminal 1 or of the Grand Arenas tram stop).