Do you feel like dancing?
'Va' is stressed: VA. 'Ballare' = bal-LA-re.
Use this when the music is good and there is space to dance. 'Ti va di' is softer than 'vuoi' and gives the other person comfortable room to decline without feeling awkward. It is the perfect dance floor invitation.
'Andare' in the expression 'ti va di + infinitive' means 'do you feel like doing something?' It is one of Italian's most useful structures for casual invitations. Compare: 'ti va di mangiare?' (do you feel like eating?), 'ti va di uscire?' (do you feel like going out?).
Vieni a ballare con noi?
Are you coming to dance with us?
Group invitation — includes you in a dancing group
Sai ballare la salsa?
Do you know how to dance salsa?
Asking about a specific dance style
Questa è la mia canzone preferita! Dai, balliamo!
This is my favourite song! Come on, let us dance!
Enthusiastic invitation triggered by a favourite song
Dancing at Italian parties depends heavily on the region and type of party. In the south, spontaneous dancing to popular music is very common. Northern Italian parties tend toward more conversation-focused gatherings. At formal dinners ('cene'), dancing might happen after midnight. 'Liscio' parties specifically for traditional Italian ballroom dancing are popular in Emilia-Romagna.