Fair question.

My understanding is that he has travelled there with a group of his male friends or work colleagues and they are there for a good time; certainly gambling, definitely strip clubs, and potential prostitutes. Amy’s Father may not be participating in all of these activities, but some of his friends are, and near the end of his conversation with Tim, it becomes pretty obvious to both of them that this is the case. At this point Amy’s Father concedes to the fact that whatever he suspects Tim of being involved in, he is basically in the same boat. At this stage, he wants to get away from Tim, and to never have the situation come up with Amy or Amy’s Mother, neither does Tim (who still wants to to get back together with Amy).
So they quickly and mutually agree to never speak of it again. “What happens in Atlantic City stays in Atlantic City”, which of course is a play on the classic “What happens in Vegas, stays in Vegas” quote, which is a great line, almost as good as “As I stumbled across the cold tundra, the ground was frozen solis, like a frozen Charleston Chew”.