Ditto what Evans said. Antigua and Barbuda are one country, and your cruising permit is good for the whole shebang.
Cruisers normally clear in in Jolly Harbour or Nelson's Dockyard in English
Harbour. As s/v Moondancer noted, you risk a very
heavy fine if you or your crew go ashore before clearing in. The crew should stay on the boat until the Captain
returns with the clearance papers. Antigua is one of the strictest countries on this sort of thing.
If you clear in in Antigua and sail up to Barbuda, intending to leave from there to sail to another country, you'll need to clear out in Codrington, which is not a very convenient place to get to from a boat. You'll need to arrange a land or water
taxi, unless you can drag your dinghy
across the sand at Nine Mile Beach on the west coast
and putt-putt across the lagoon
to town. Don't do this if a swell is running. We had planned to clear out there, but a northerly swell was running, so we couldn't land the dinghy
. The swell was forecast
to continue for several days, so we just left without clearing out, since we needed to be up in the BVI to meet someone. Caught hell from C&I in St Maarten for not have outbound clearance papers, but managed to avoid boat confiscation, fines, and jail time by smiling, nodding and appearing suitably contrite.