There are a few options around the airport (including a Radisson immediately nearby) but I would not finish an evening of music and fun with a night at the airport

I would recommend staying downtown instead; the journey to the airport from center city is 15 minutes, more with traffic, and MEM is a small airport where check-in and security are usually a breeze.

I have never stayed at the River Inn so can not comment on the quality, but the location is very quiet, on a little island called Mud Island; I only remember one bar / restaurant on the island. If you want more animation, I'd stay at the famous Peabody Hotel or somewhere nearby (DoubleTree, Holiday Inn, Westin and more) to have some ribs and listen to music at BB King's, walk down Beale Street or enjoy a beer at the Flying Saucer (300+ varieties)

Cheers,
J-