There's an approximately 24"×24"×32" space in the corner of my kitchen between the actual cabinet and the range.

I'm at a loss. The house is fairly small, and I'm an efficiency nut, so 10ft³ of totally useless space bugs me. The proximity to the oven would make extending the cabinet back that way and using some kind of blind-corner storage solution impractical.
We've been thinking about getting a new water heater, the current one is ancient and lives in a little enclosure outside, about 12' away. Can we get one of those short ones and tuck it in there or is that likely to overheat?
We've also been talking about a whole-house water fountain system, but I'm worried that changing filters would be incredibly annoying.
What's on the other side of that wall? Maybe that room could use some extra (secret/hidden?) storage.
I was thinking about that. On the other side of the wall opposite the range is a little linen closet/alcove. It's pretty narrow, so it would be a bit awkward to access, but it could work for extra pillows and comforters. It's certainly an option to consider.
That sounds like a good option. Might be a good place for sneaky storage.