I dance. But I'm quite unclear of what you mean by social dancing that doesn't involve ballroom dancing. There isn't much left.
I do latin: salsa, rumba, cha-cha, mambo, samba, and if forced I'll dance mergengue.
I do smooth: foxtrot, waltz, vieneese waltz.
I do swing: single time, west coast, and a bit of triple time, double time, and lindy hop, hustle.
I do tango: argentine is my favorite, but I'll do stanard tango as well.
Then I'll occasionally do a bit of other dances but I don't really know them: quick step, polka, line dances (if forced), several country dances (if forced), passo doble, nightclub twostep, and the minor variations of those above.
But since you hate those dances, I can't think of much left that you'd like.