There is really no place guaranteed to see the turtles. They come in and in the middle of the night then the nest is very well protected by the Park Service until the eggs hatch and the babies return to the ocean. This happens on Hatteras Island and Ocracoke. The horses (and turtles) are up in Carova, four wheel drive territory. If you want to be close by, and do not have a four wheel drive vehicle, you might consider Corolla. Note, however, that human interaction with the wild horses (and please note "wild") is strongly discouraged. No feeding, chasing etc.
For me to tell you when and where is very difficult. You may want to contact the Park Service to get a better idea on the turtles and the Corolla Horse Foundation on the horses.