The castle is on the north side of the entrance road (only paved road) into the park. There even is a sign. But the best bet is to drive on past, get out of your car and start walking. That approach will provide multiple image opportunities.
In the spring, storm clouds arrive quickly and offer dramatic back grounds and great lighting in Capitol Reef National Park. During a five day stay, I waited every morning and afternoon for the right combination of clouds and light. The Castle is one of those remarkable formations that look good in any light but when you throw in clouds as filters the result can be awesome.