Hi there. How do you plan to use the phone? Do you need to make a lot of phone calls? Or just data, mostly?
AT&T's international plans are not cheap, but the $60/month plan (1GB of data, free texting, 35 cents/min calls) is probably adequate for the average person. 1GB would be not quite enough for me for 16 days, but I could probably stick to WiFi most of the time and conserve and get by, use the mobile data only for walking directions and public transit info (don't need mobile data for GPS if you are driving with Google Maps "offline" mode.). Calls home to US numbers are free (even to landlines) with Google Voice, plus you could try to set up WiFi Calling to make free calls home. Install WhatsApp to make calls to locals in Europe - it's popular there.
Or use the $10/day plan - charged only on the days you need it. Obviously, if you use it more than six days it costs more than $60 for the whole time.
Buying a SIM in Germany is not impossible but can be complicated. Germany requires a local address to buy a SIM; people seem to find a way around it (use the hotel address?) but it's more difficult than in other countries.
One option is to buy a SIM for another EU country that lets you use the SIM in Germany. I've had great luck with my Dutch Vodafone SIM for use elsewhere in Europe. I bought it on eBay - haven't used it in the Netherlands yet! It's mostly a good option for data, not for calls. But I use Google Voice for my calls anyway. You can get 6GB of data for 20 euros good for a month - should be plenty for your trip. SIM costs currently about $11 USD shipped to the US with no credit on it.
But your phones must be unlocked; if you bought them from AT&T they probably aren't and can't be unlocked I believe until they are paid off.
And if you do manage to use a foreign SIM, know that you won't have your US number while the SIM is in place, until you put your AT&T SIM card back in.