Oh man, I have this problem to a high degree. Almost anywhere outside the home I'm embarrassed to masturbate. I feel this way at the grocery, the laundromat, even dentists office.
Hospitals are intimidating, so it's a great place to start, but there are lots of places we should be putting these. Hopefully they come out with a portable version to make this something that we don't need to be embarrassed about anywhere really.