In Antigua, I highly recommend taking a tour with Lawrence of Antigua. (website www.lawrenceofantigua.com
) He has a spotless air conditioned van, is very professional and will recommend a couple of touring options to you. He is very responsive to gearing the tour to your wants and interests. I recommend a tour that includes Nelson's Dockyard and the National historic Park (the dockyard and the various hill fortifications around it). The National Park is very well setup (one admission - $5 includes all the sites). There are guided tours at Nelson's Dockyard and at the Dow's Hill Interpretation Centre (also a multi-media presentation at Dow's Hill). The views from the various hilltop sites are spectacular.
In St Maarten, I recommend Orient Beach. Great beach, lots to do, good restaurants, great people watching.