I've been to Germany quite a few times.
I wouldn't worry *too* much about having a chip-and-PIN card. I've used my chip-and-sig cards and even my swipe cards (debit and credit) throughout my trips at hotels, hostels and on bigger purchases (like pricier gifts), and at airports. Actually, even on my card that had the chip, the person manning the hotel front desk ran it through the swipe reader the second they saw I was American and had a stripe on my card. When the machine prompted for chip, they were like, "Oh" and used the chip.
The only time I got stuck was (surprise surprise) trying to buy train tickets at an unmanned kiosk in a non-major train station at night. It rejected my chip and signature card. I had to hoof it back to the hotel, which, luckily, had the local metro cards for sale at the front desk.
In general, Germany is a more cash-based society, so you'll probably get your card turned down (whether it has a chip or PIN or not) at restaurants, food stands, small shops and day-to-day things. I speak German, so I pressed the issue a few times when I was short on cash, pointing out that I'd seen a German customer use a card at that very restaurant five minutes ago, and the waiter got super huffy. So, always have cash. Also, expect hotels and hostels to charge you a fee for using your card to pay for your room.
As for ATMs, Deutsche Bank charges no fees if you use a Bank of America card. Deutsche Bank is practically everywhere, so this is super handy. HOWEVER, lots of German ATMs (even in major cities) are inside the bank lobby. And banks are closed on weekends and even late afternoons sometimes. You have to use a Deutsche Bank card to swipe in, and, in my experience, your BofA card won't work for that.