On the town means out enjoying the bars and clubs of a city. A night out on the town.
A night on the town is a whole evening rather than one stop. To go out on the town is slightly old-fashioned and entirely cheerful.
1phraseon the townOut enjoying the bars and clubs of a city.
“They went out on the town and came home at four.”
on the town is a phrase.
Practised in Idioms