Hi Nancy,
If you are unable to swing the Grand, check out Hilton Stockholm Slussen. We stayed there, prior to our Baltics cruise, using HH points, as the hotel chain I work for does not have a property in Stockholm. We were pleased with the accommodations. Not as upscale as the Grand, but perfectly fine, clean and well located.
I don't recall the airport being terribly far from the center of the city where we stayed.
