I left my engagement and infinity rings on, and they were on the same finger as my wedding band. No one said anything. I did put my expensive watch, earrings and necklace in our locker. I felt it was safe, and everything was still there, where I put it, when I opened the locker to leave. So, I would not be worried about putting jewelry in your locker. I would not leave it in your hotel room. If you don't want to take it with you to DC, then ask your hotel's concierge to put your items in the hotel's safe.
Have a great time, we really enjoyed our times at DC.