"The bathroom is over there."
I suspect it's the equivalent difference between "The bathroom is over there" and "There is a bathroom over there"
あります literally means "to exist" so using です declares that over there is bathroom while あります says that over three a bathroom exists. So I would say your translation is a perfect translation
This is what i thought it was as well. People were saying there is a difference between the two and this doesnt seem to fit their explaination
"As for over there, it is a toilet." That's how I interpret this answer. I imagine トイレはあそこにあります would be more like "As for the toilet, it exists over there." Is that accurate?
I'd basically agree.
トイレはあそこです。 The toilet is over there. Lit. As for the toilet, over there is.
トイレはあそこあります。 There is a toilet over there. Lit. As for the toilet, over there exists.
あそこはトイレです。 Over there [that] is a toilet. Lit. As for over there, toilet is.
あそこはトイレあります。 Over there is a toilet. Lit. As for over there, toilet exists.
In American English, we use "bathroom" to mean both a place where there are toilets and a place where there is a bathtub.
Yes, it should be place wa room ni arimasu. Naninani ni arimasu is a set locational construction. Desu is the verb to be so if you use desu you are saying "it is a bathroom", not where a bathroom is or if there is one.
The commonly used (and politer) word for bathroom/toilet - that I know of - is otearai 御手洗いhonorific お, 手 hand and 洗い wash - so quite literally - the place where you wash your hands - you may note that arai looks like sen from sensei except that it has suihen on the left - in other words the radical on the left is from mizu/sui water - could be helpful for remembering. In my experience トイレ is rather informal, not as polite and can be used as a colloquial way to ask someone if they want to have a fight/step outside - トイレ？トイレ！