In 2011 my wife and I took a trip to St. Croix during October. This is off season and we got a fantastic deal on both flights and hotel lodging. Honestly this is how we normally travel since it saves us a lot of money. We stayed at Chenay Bay on the north west end of the island at the Chenay Bay Beach Resort which was a great location. Throughout the week we spent a lot of time both going snorkeling and driving around the island to see different towns. Since it was off-season the island was almost dead from a tourist perspective, but the restaurants were open, and everything was available.
Down in Christiansted Harbor you can find the Danish Custom House located at the west end of the harbor district. On the day of our visit they had the doors open which gave the impression of looking through the door at the same door.