Characters
We'll do the town one night on me.
— Dick Stensland · L.A. Confidential

Behind the line May contain spoilers.
Our reading
An editorial interpretation.
The speaker offers to treat someone to a whole evening out, with the speaker paying for it. It is a breezy, open-handed promise of an evening's fun, offered as a treat rather than a debt, and confident in its own generosity.
Context reviewed