Out of Eretz Yisroel there are those that do Hakafos on Shmini Atzeres at night and some that even do it by day. Mostly I think it is by the Chasidim. Does anyone know of any Yeshivish or non Chasidish place that makes Hakofos on Shmini Atzeres?
Yeshivas Chaim Berlin, as litvisha yeshiva on Coney Island Ave. in Brooklyn, does hskafos on Shmini Atzeres at night. They come back to the yeshiva after eating the seudah and the Rosh Yeshiva speaks (gives a maimar) in the sukkah. Afterwards they go inside and dance hakafos. The hakofos usually do no start until 2-3 AM.
I've been to multiple congregations that use Nusach Sfard but aren't particularly Chassidish that do Hakafot both nights.