We usually go over NYE every year and have a crew of friends who do the same.
The price is the highest of the year, and many villa and hotel have min nights (10-14 nights). We like to go for two weeks so that doesn't impact us.
If you have fav dinner places-make those reservations when you book your villa or hotel.. Why wait to make a reservation when you know you want to go? Maya's, The Strand, Wall House, and Le Ti St. Barth's are very competive to get a table during that time period.
It is the busiest time period, but even then, the beaches aren't crazy cowded.
And star sightings are a fun bonus.