Munich has a very useful advantage for people in this situation: transit service from the center city to the airport starts VERY EARLY in the morning. IIRC, on weekdays, the first S-Bahn train leaves the Hbf at around 03:45. This makes it practical to stay in the center city and still arrive back at the airport in the morning of departure with plenty of time to spare.

It's surprising how many major cities don't start transit service to their airports until later in the morning.