OK, with those times here's what I would do.
First, you're going to want a place to sleep, so find a place near the airport and make your reservations. Ideally find a place near the U-Bahn line. Plan to go and check in and drop your luggage. (It would be even better if all you have is a carry on and your larger pieces can be transferred direct to your next flight, then you could call ahead and let them know you're checking in late and just head into the city.)
If you haven't been to Munich before you definitely want to get into the old (touristy) part of the city. I'll assume you're traveling this summer, so it will be light outside until @ 9pm. If you're able to take the U-Bahn to the main Bahnhof it's a easy 10 minutes walk from there into old town. If you can afford it a taxi (from the airport) is better, but they're not cheap. Walk around, see the city, do some window shopping, listen to the buskars playing in the street. (Munich has a very good musical university program and there's a very good chance to hear world class music just walking around.) Find a place to eat, outside should be best if the weather cooperates, walk some more (realize the major tourist stuff closed before you landed) and then head back to the hotel and crash for a good nights sleep.
If you know Munich then you have a choice to stay local (around your hotel) or go into the city. But if you've never been there you should definitely take the time to explore.
I will suggest you avoid the Hofbrauhaus, or any of the "big name" places to eat. They so rarely live up to expectations. You might ask a local (look for a student, they most likely speak English and know the good, cheap, places). Remember the menu and prices are displayed outside so you can look before you decide to enter.
If you pull up a map (google is good) you can easily trace out a path around most of the old city center that shouldn't take more than a couple hours (max) and still let you see the majority of the area. Much of that part of town is closed to vehicle traffic, and after 6pm stores start closing down. Still, old town Munich, like many major European cities, has a life of it's own after working hours.