I do believe that narrow ledge shelves with pics propped on them would work the best. You still need to be able to use the thermostat and could reach behind. Just keep them narrow so you do not run in to them. Layer things instead of lining them on when you are deciding on decor for them. Maybe try two and have them lined up straight up and down from each other.

Oh, never ceases to amaze me when a wall made for displaying art is "occupied" by a badly placed switch/thermostat,whatever right in the middle!" This can happen even when electrical plans are explicit--at the moment, someone thinks they know better.

Depending on your general decor, an alternative to the good idea of offsetting horizontal ledges might be to build a floor to ceiling unit for shallow storage and display of collectibles. Good luck!

The first thing I would do is hire an electrican to move the thermostat ove to one side or the other so the wall is usable. You'd have to have the hole patched, and repaint, and then you'd have a usable wall.

I would put a nice picture there. Since the wall is a little bit narrow, I'd go with a portrait orientation picture about 18x24" with a matt and frame.