Yes, go for the city, that is the best way to kill the time.
If you are not up to it, however, it must be said that T2 at MUC is one of the nicest terminals around and if you go landside, there is also the plaza mentioned.
An alternative to the train is the Lufthansa Airport Coach:
https://www.airportbus-muenchen.de/en/ It goes to the central railway station and is 17 EUR return.