An additional neutral and more up-to-date indication for network coverage is http://en.netmeterproject.com/ - after selecting Germany in the upper left corner you can view coverage maps of all four German networks gathered by end user devices. Hence you can only see trails of where users have moved along but not any covered surface areas. As this data comes from real life phones you can often see new LTE deployments sooner than official coverage maps show but it does not represent coverage areas, rather a collection of spots from which you can estimate network availabiliy.

Excellent information, thanks for the all the help.

So has the OP actually been able to use one of these prepaid products in Germany yet?

By the way, what I mentioned before is about to become reality from April 15th: o2 and eplus will open up their 3G networks for mutual roaming. Apparently SIM cards are already receiving OTA updates changing the network aliases. In case of the MVNOs eplus and o2 now both appear with the identical network name (e.g. "simyo" and "simyo"). In contrast SIM cards directly issued by o2 and eplus will indicate the newly accssible network by a plus sign ("o2-de+" or in case of eplus which during the last years used the "base" brand "base.de+").
This only applies for their 3G networks. For 2G there will be no roaming as coverage of both networks is considered as being on par while for 4G there will be no roaming either - probably because of the complexity of implementation which does not pay off given the comparably small 4G footprint of eplus.

For furher details read http://www.teltarif.de/e-plus-o2-nat...ews/58878.html (German only)

Prepaid Wikia indicates that Simyo SIMs are available at Aral and Shell petrol stations and the DM drugstore chain.

Do these places stock nano SIMs?

Hi. I'm not very sure about this info. Generally, SIMYO is mostly an offline MVNO who sends the SIM cards by mail. This is true to many countries like Spain.

In Germany they tried to sell it in some stores at least some time ago. But they are rare in shops. The German Prepaid-Wiki says, they are online only.

To order it online, you need a German postal address or you order them from Ebay or Amazon unactivated to be sent to the US.

I'm going to check some Shell or Aral stations if they are still sold. If they are not sold offline anymore, I'd need to take SIMYO out of the prepaid data wiki. Because SIMYO has a lot of fans, I need to be sure first.

As SIMYO sells online only mini/micro OR nano cards, i'm pretty sceptical that you can find it at Shell or Aral anyway.

If it helps to you: Ortel Mobile (another MVNO on eplus) I bought recently at Shell. They sell hybrid mini/micro/nano cards.

Are Shell petrol stations common in the center of Munich?

My hotel will be near Hauptbahnhof Platz.

Otherwise, I hear there are some Handy shops nearby one of which may sell Blau SIM cards and supposedly have helped tourists register them.

There are also Vodaphone shops too, though those seem more pricey if you add 1 GB or more data. But for good LTE, it may be worth it.

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.

I may do some day trips, 2 hours on a train each way.

So maybe better odds of getting an LTE signal on Vodaphone?

My iPad mini2 supports bands 3, 7 and 20.

Vodafone has a widespread coverage of LTE on 800MHz band, which makes it the better choice for travelling than eplus with patchy 1800 MHz LTE coverage.