English Translation
Where is the bathroom?
(formal to a stranger) お手洗いはどこでしょうか? (pron. おてあらい)
(formal to a stranger) お手洗いはどちらでしょうか?
(very casual between friends or family members) トイレ、どこ?
are much better for two reasons.
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でしょうか is a polite way of asking to a stranger. トイレ as a loan word from “toilet” is too direct and doesn’t fit the whole sentence…
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あるのでしょうか? is wordy and exaggerated too much, meaning “I am wondering where on the earth a bathroom is”. どこにあるのでしょうか? sounds natural in the context of “Where is the justice?” in a condemning tone, for example. The connotation is “it is very hard to find it”. So, トイレはどこにあるのでしょうか? sounds like the speaker being solo in a wild desert, a ruined site or a huge castle, and difficult to find a bathroom.