What are your interests? Is the child a boy or a girl?

The best sight for kids (boys in particular) in Munich is the "Deutsches Museum", either the main museum, or the Verkehrszentum: http://www.deutsches-museum.de/index.php?id=1&L=1

The problem is that both the main museum and the Verkehrszentrum (cars, trains etc) close at 5PM. However: Munich is a nice city just for strolling, and an evening meal in a beer hall (preferably the Hofbräuhaus) will also be appreciated by kids. June is a fine month for strolling. Walk around downtown, and you will have a fine evening.

I would not plan on anything other than a good breakfast at the hotel before heading out to the airport again next morning.