Are there culinary uses for the water left from peeling almonds?
Generally, there is no reason not to use it. However, I'm hard pressed to think of a good place, generally because good cooking prefers other, stronger flavored liquids instead of water. 

An application where you can have the flavor on its own would be making ayran or a lassi. I think it would be an improvement over plain-water-ayran. 

For other uses, just substitute plain water to get a slight nutty hint. I like to pair rice with nuts, so you could use it instead of pure water to cook rice. Or add it to a pot of stock you are making - with a complex stock of a meat and several vegetables, it will be too subtle a taste to register consciously, but will enrich the flavor as a whole. For a simpler stock (e.g. just chicken with classic mirepoix) the taste of almonds can get too strong, depending on the quantity you use.