My wife and I are looking for a place to stay for 2 nights close to the middle of the city for under $100 a night?
a nice and budget place to stay is the Hotel Motel One München Sendlinger Tor which is a chain and offers a decent comfort for an affordable price. They have several locations in Munich, so you can decide where you prefer to stay (for example the one at Sendlinger Tor) ;-)
Wish you guys lots of fun in that awesome city :-)
Check out airbnb- I usually find great places at great prices in very central locations.