At the airport, shops and lounges. Boring. If you are into Geocaching, there is a TB Hotel right at the airport.

Depending on the time of day and day of year and the weather that day, you may find it enjoyable to go downtown. It's easy. Take the commuter train (S-Bahn) to Marienplatz and enjoy the sights and the people. Walk to nearby Viktualienmarkt for a beer.

If you are into BMWs, you can go to the BMW Museum. No direct train from the airport, but you can get there easily from downtown on the U3 subway.

If you are into Audis, they may still have a show of the new A1 in the plaza outside the terminal. The A1 is as unexciting as an Audi can get.

Savings tip for going downtown: make sure you get a day ticket. It costs €10,40 and is good all day, covering your trips out of the airport and back, as well as any in the city. This is a much better deal that the single one-way ticket for €9.60. Better yet, if there is more than one person traveling together, get a group one-day pass for €18.80 which is good all day for up to 5 people traveling together.