Two Antigua marinas
I've stayed in both Jolly Harbour and Catamaran Marina. Their dockage rates are not that different, on a monthly basis. JH has moorings for $15/night. I can't say which I prefer--Jolly H is in a cozy little cul-de-sac surrounded by residential properties; Catamaran is open to Falmouth Harbour (cleaner water). I think I'd pick Catamaran--it's a half mile dinghy ride over to English Harbour town. My sailboat is stored in Catmaran owner Hugh Bailey's boatyard right now, waiting for hurricane season to be over.
Check the websites; the rates are posted there:
Nevis, West Indies
p.s. have you thought about St Lucia (Rodney Bay Marina)? It puts you closer to the Grenadines, Martinique and Dominica, some great spots to visit.