There's an interesting BMW museum. Don't miss the main square, where the Hofbrauhaus is located.

Airport hotels charge for their airport shuttles, IIRC 6 Euro per person.

There's a nice (but not particularly cheap) hotel right in the airport, the Kempinski. It has an indoor pool, restaurant, etc. There's also a brewery and biergarten/restaurant/bar right at the airport, in a courtyard with a bunch of shops, including relatively big grocery store and drug store. In fact, for someone who has already seen Munich, staying at the airport wouldn't be bad at all.