Yes you can just walk on the paved road west and up. Steep but doable and probably 20 or 30 minutes up to where you have some nice views. For the last few years we have hiked over the top from Diamond Cay to White Bay. Steep ups and downs. Takes a few hours and you need to take water because it is hot. The views are awesome. The reward at the end is usually some cold drinks and lunch at Hendos. Then a cab ride back to the boat at the other end of the island.