You could try salsa.
But often the problem is not the culture of the music, but a rejection of the ballroom idea of cooperation in movement. Someone who wants to just go out and move on their own is taking a very different approach to dialogue in dancing than the approach at the basis of the partner dances. You can ultimately end up in the same place and achieve interaction, but the steps along the way look very different - in ballroom its cooperation first and dancing second, in popular dances its dancing first and cooperation second.