That's a great neon sign! It probably pre-dates the one that was on the hardware store I worked at, which was from the late 40's - early 50's. I bet the American Sign Museum would like that, if they don't have one already.
The sign museum in Cincinnati has Neonworks, its own neon shop. I haven't been yet, but one of my buddies knows the guy that started it. With Frigidaire having been based in Dayton, they may be interested if they don't already have one.