Nearest entrance to the main park can be found by searching Porta Grande Bosco e Museo di Capodimonte.

This fountain in a round about is nice and all, but it's probably not what you are searching for when looking up Capodimonte, even if it's not technically wrong.

If you are searching for the big park to visit, this is down the hill from it. On the map, it's just to the right and has a couple large buildings. It's a bit of a climb from this round about to there and the buses can make it almost directly to that entrance.