The Key Cay anchorage is pretty easy anchoring with good sand holding, but the last time we were there in December it looked like someone was putting in a bunch of mooring balls so not sure if it is viable anymore. any heavy SE swell or wind i think could make it a pretty uncomfortable night.
The anchoring between Eustatia and Prickly Pear also has good holding in sand and is pretty comfortable in normal wind conditions. Have been there by ourselves and with as many as 5 other boats comfortably spaced. The reef offers good protection from all but a strong NE swell. The entrance to the north is pretty straight forward if you pay attention to the charts and steer clear of the reef extending from the north side of Eustatia to the west. You will likely have a few local boats run through the area behind you at fairly high speed though so just be aware.
White Bay on Guana has like 5 balls but not sure of their restrictions if you want to go ashore.
Diamond Cay has plenty of balls so I wouldn't call it secluded but is a fine anchorage to overnight in most of the time. For seclusion on JVD, would try Little Harbour as it tends to be much less crowded and a couple of classic restaurants to eat at as well.
Never overnighted at Long Bay so can't comment there. Love Savannah Bay as we almost always have the place to ourself but it is redlined for many charter companies.