Nicest sailing area - there are many! The Grenadines and Virgin Islands are probably the most popular, but all of the islands are very different and have their own characters.
It depends on what you want. If it's good sailing you're after, probably the BVIs. If it's interesting places to visit then the Windwards and Leewards. The Windwards are more scenic being steep with rain forests whereas the Leewards are flatter and dry/scrubby. The former British islands e.g. Dominica are more 3rd world while French islands like Martinique are more sophisticated.
Would you prefer a beautiful anchorage or a busy marina with lively bars? Do you want to eat West Indian food like rotis or would you prefer a restaurant serving lobster and fine wines?
If the thought of boat boys puts you off, go for the Leewards.
Tell us what you are looking for and we can better advise you.
You will probably like the southern islands. The Tobago keys, Bequia and others around the Grenadines. Probably the most beautiful anchorages in the Caribbean are in St Lucia: Marigot bay and the Pitons.
Further north there is Antigua with Great Bird Island and English Harbour, Barbuda with the 11-mile beach, Montserrat and St Barts with Anse des Columbiers, my personal favourite.
Interesting comment re boat boys - not put off but just don't know the right protocol. What is the best way to respond, bearing in mind not all boat boys are the same?
Just left St Barts and Anse de Colombiers - very pretty and quiet but if you are going to charter you have to be a bit pragmatic about wich Islands to use. Sunsail and the Moorings are well spread out but tend to focus in key areas. Antigua (where we are currently) has plenty of variety good airport for UK direct and Sunsail are in English harbour. Probably a good bet. BVIs are nice but completely swamped by charters, all the bays have moorings which is OK but means you can hardly anchor anwhere. Of course for a week this may not be a issue.
The way to deal with boat boys is to be polite, never rude or dismissive. If there's nothing you want to buy say 'maybe tomorrow' rather than 'no'. When it comes to people demanding money for handling your lines or pointing to a buoy, make sure you appoint one person, never let several join in or they will all want the money.
Never pay anyone to take your rubbish away, they will tip it out on the beach, take what they want and leave the rest to blow round the island.