I'll add another vote for the Abacos as a good location to meet your needs. Marsh Harbour is a good place to fly people in and out of, and most locations in the southern Abacos will have subscription Wifi access, or you can get it at many establishments.
The Abacos also have many uninhabited islands, not far from the small towns, etc., so you can spend a lot of time at them without being too far from the phone and Wifi services you demand. Even when I chartered there a year ago, we had an anchorage to ourselves every
single one of the 9 nights we were out. Of course, the northern Bahamas are even more
remote. The Carter Cays Group, Strangers and maybe Great
Sale are about the only places I didn't get
cell phone reception. Depending on your intended use, you can either pay the international fee for your U.S. phone or
purchase a Bahamas plan there, either switching your sim card or just
buying one of their phones. (I had my old
Iphone unlocked before going there, but despite a new card, could never get it to work on their plan.)
Two day
sails from the southern Abacos will also get you to the northern
Exumas, if you want something more.
I recently sailed the Bahamas from Mayinagua up through the Abacos, and despite being so close to
Florida, I think the Abacos have more uninhabited islands and anchorages you are likely to have to yourself, than islands further south.