The business that Rain had in America seems to be attending the Grammy Awards!
Rain and his wife Kim Tae Hee had traveled to America for some personal business, and it looks like that was to attend the Grammy Awards. He posted a photo of his invitation ticket and the stage at the 59th Grammy Awards. Most likely, he's there with Kim Tae Hee as well for an incredibly unique experience that most K-pop stars don't get to experience.
Hopefully, they're having a great time!