Want to go see a movie tomorrow night?

Literal

Tomorrow [possessive-の] night, movie [to-に] not-go?

A casual invitation built from a negative question (行かない?). Japanese regularly uses the negative form to soften invitations and suggestions — asking 'won't you?' instead of 'will you?' is friendlier and more tentative. The rising intonation (?) makes it an invitation rather than a genuine question about non-going. The particle に marks the movie as the destination of going, not を as the object.