。
Would you like to go dancing?
Literal
Dance [to-に] go-not-[question-か]?
~ませんか is the polite negative-question invitation form — 'won't you...?' 踊りに行く ('go dancing / go to dance') uses the masu-stem 踊り + に + 行く, the standard purpose-of-motion pattern: the に marks the goal of the going.