[wolfbln]

Vodafone or other MNOs are over here more expensive than the MVNOs or resellers. You will get LTE on Eplus in downtown Munich too without a surcharge on its MVNOs. But it might not so easy to find a nano SIM right away at the first shop.
When you leave central station towards Karlsplatz (Stachus) just check a few of the phone kiosks displaying the logos of the companies. Some operators now sell triple hybrid cards, at big network operators you'll find a nano for sure. In this area you have plenty of choices, but not so many gas stations.
Be aware, that LTE is on Eplus on 1800 MHz or Vodafone on 800 and 2600 MHz - other frequencies used here than in the US.

The small "Handy" shops may help you with registration. This is now done online and you need internet like a WIFI for doing this. So you might do it at your hotel. Just look for a valid German street address with ZIP code like your hotel address as you need to give a German address. Activation can take an hour or two.