Cheap Trick is one of the greatest bands to ever come out of the midwest. (Chicago-area, I believe.)
They're a LOT more than "Don't Be Cruel" or "The Flame." Those are good songs, but they have dozens and dozens of great, great songs.
As someone said, "Surrender" is probably Cheap Trick's best - and one that I consider maybe one of the best rock songs ever.
"Southern Girls" is incredible. So is "I Want You To Want Me," (That's the one everyone knows from the Live at Boudakon album) "If You Want My Love," "She's Tight," "Up the Creek," "On Top of the World," "Mandocello" - the list is very long.
Definitely check them out. They are a great band.
I've seen them four times over the years, and actually hung out with them a bit when they played Hampton Beach (I was a bouncer at the club.)