In between to your seat and the window is the best move.
I had no issues with a 36"x24" oil painting, framed with glass, in between 2A and window on SFO-JFK, nice and secure.
For added discretion, if preferred, you can just cover your window armrest with a jacket, and FA won't even know it's there.
Since you're on the 737, there's also the option of the F coat closet.
If you go the overhead bin route, aim for the aisle seat beneath the bin your fragile item is in, so you can politely alert folks if needed when loading/unloading.
Pleasant travels!