There is nothing like an onsen trip and it looks like your's was no exception. I feel so robbed growing up in the states without them. Did you have to go outside your prefecture to use the GoTo? I'm heading back to Japan in just over 1 week and I'd like to take a vacation with some of that GoTo funny money.
One of my very first experiences in Japan was the public bath. I was staying in at the Yoyogi Olympic Hostel I think and the bath was communal. Just had to let the freak flag fly and do my thing. None of the other dudes seemed to give a shit so the awkwardness went away after the first day.