The best two days are the last, being the first Monday and Tuesday of August which are public holidays. Monday is Jouvert Morning and Tuesday is Last Lap. Very very early morning parades through the city of St. John's the capital.

http://antiguacarnival.com/

http://www.antiguanice.com/v2/client.php?id=454

I lived there for 28 years until recently, never went once. Not my cup of tea I'm afraid. You tend to see more locals and returning Antiguans and Barbudans than tourists at the shows and parades.