I suggest visiting castles when they are closed for the best pics. Berg eltz taken on Christmas eve this year......

If anyone was interested in more than just the name and the fact it was closed when OP visited: Here (in English)
It's on the Rhein, south of Bonn and west of Frankfurt in Rheinland-Pfalz. Near Wierschem, the closest city is Koblenz which is well worth visiting for the views from Festung Ehrenbreitstein, which is reachable by cable car across the river. Burg Lahneck is also a good sight.

My favorite castle in Germany. I've been a few times and I really just love visiting it. I used to fly in a helicopter over it all the time as well, a truly great view. I live out in Bavaria now, so haven't been in quite awhile, but it's such a great castle.

A good strategy for that in Germany is to go first thing on a Sunday morning. Historical attractions and museums etc. are (normally) open on a Sunday when most other things aren't. It's normally balanced out by them being closed on a Monday so I'd recommend checking before you visit somewhere.
I recently spent 4.5 hours hiking to Ruine Krukenburg to find a sign saying it would be open in March.