Were this the 1880's and you were in NYC and invited to hunt the elephant it would not involve guns and safaris. Well safaris anyways. Hunting the elephant was slang for going to the "bad" parts of town, lower eastside, Bowery, Chinatown, my brother's apartment, etc. to take part in the fun, er, decadence that every other building seemed to offer. Drinking, gambling, carousing, can-can dances and all that other stuff we're not supposed to want to do.
Good, we each learned something today.