There are actually two casinos nearby, Foxwoods and Mohegan Sun
They are kind of expensive if you just want lodging. But fun anyway!
Closer to the Academy there is a Holiday Inn which is good. Several nice motels in Mystic, fairly cheap this time of year.
I've never heard of visitors getting mileage but I could be wrong. Maybe it's an official football visit which falls under NCAA rules.
Anyway dress warm it's been pretty cold up this way. Enjoy your visit!