Antigua is not a large Island. There will be a stage when one will feel local offerings become slightly stale, and when the idea of beyond will become equally more appealing. 
Luckily, hoping to even smaller islands, like Montserrat or Barbuda is not that difficult.  There are irregular ferries and flights available to make these short escapes possible.
Barbuda is flat as a pancake, and there is little to attract land-lovers.  Beach and sea enthusiasts will love the tropical waters and the white shores.
Montserrat is an active volcanic Island, paradise for land lovers and not quite as exciting for sea & beach buffs.
Last, Redonda is  a rock of no interest to beach lovers, but a uniquely isolated spot where to enjoy nature at its best.