I was considering adding stargazing as a synonym for “moon viewing” because I’ve never heard someone use this term in English before. Stargazing seems like a more natural translation, but I don’t know if this is a correct translation. A quick search on Jisho brings me to only this:
放心状態 - 1. being in abstraction; being dazed; being absentminded; stargazing
Would I be incorrect to associate 月見 with stargazing?
In Japan there is a tradition to enjoy looking at a full moon during mid autumn. It’s called 月見. Originally to celebrate harvest. It’s like a harvest moon festival. I think it’s better for you to memories moon viewing as Japanese tradition like 花見.
Moon is a big part in Japanese concept of beauty. You would often see that word in menu as well. Such as tsukimi udon (udon with round egg yolk topping) , tsukimi dango (a rounded sweet cake).