Been to the Azores twice, the second time being the honeymoon 21 years ago, and I couldn't agree more, we regularly talk about returning - except that it will be for more than the 4/5 days I have available this time round.
Have taken aboard all the comments but continue to do the research. Would be travelling on BA concessionary tickets so the fare is immaterial but I am more than shocked at the £80 price tag for two roundtrips Heathrow-Gatwick.
Grand Cayman also fits the calendar constraints, and it's a Heathrow departure, but it means a deeply unromantic 06:50 departure on the first leg, and a long day's travelling thereafter. And hotels there seem to be considerably more expensive than BDA.