Many who visit Anguilla find a way to spend at evening at The Viceroy's Sunset Lounge.
While it's not typical Caribbean style or unique, like many of Anguilla's night spots, it is beautiful and offers sushi, small plates, and cocktails.
Check The Viceroy for a live music schedule as it tends to change often. There is a popular and fun dj there for dancing sometimes too!
A newer establishment for late night in Anguilla is the Velvet Lounge. It's located in The Valley above City Liquors.
While they too can have quiet nights, they stay open late. They also usually supply a DJ or have a local soca band to perform. Local soca band performances tend to not start until after midnight.
You won't see many, if any, tourists here so if you like the "off the beaten path" style, enjoy getting to know the locals and are a night owl... Velvet Lounge something to consider.
It is a dark place with a club-style approach with a friendly staff. The music tends to be very loud so this wouldn't be a place for too much chatting, unless you like to yell!