Update June 6th 2020: The container has been replaced by USa68. Many thanks!
The best way to do this cache is to hike starting in Termini. If you follow my suggested route, plan on taking an hour to get to Punta della Campanella and a bit less than two hours to get back. The difference in altitude is about 300m.
When reaching the bus stop/parking (see waypoint), go to the other waypoint indicated in order to obtain a free map of this hike. This will be helpful if you don't have any trails on your GPSr (or if you have one which doesn't display maps). You will also find a porcellain plan of the starting area.
I suggest following the yellow trail #1 to get to Punta della Campanella and taking the red 00/Yellow #2 trail to get back.
At the cache location you have a good view on both gulfs as well as on Capri.
Logging should be quite easy, even though this place seems to be quite frequented by locals as well as tourists. The cache is just a little bit away from where the lighthouse is.
And this is what it looks like from the other side - from Capri (far away, on the top left):
Warning: The cache itself is near cliffs with a steep and deep fall into the water. Watch out when searching and keep children from going too far out.
Many thanks to indiana_jade for replacing the container in April 2015!
Many thanks to USa68 for replacing the container in June 2020!