If you want to "drop off the face of the planet", then Comoros is quite the place you have been looking for. This is a reserved archipelago that is found in the eastern part of Africa. It is located in the gulf stream of Mozambique and is quite beautiful to actually visit.
Here are some of the places you could give a try.
This is the smallest island in Comoros needless for me to say, it is quite pristine. The island is inhabited by a few people a d it lacks most modern ammenities. It is the only island where you will find the national park and it is exactly the place for nature lovers.
From this island you can see aquatic wildlife such as dolphines, turtles and occasionally sharks.
If you have had the chance to go through the novel Robinson crusoe, then this island will make you feel like you are in the same book. It is referred to as "the pearl of Comoros ". This is because the island is quite reserved and still has the arab cloves plantations and a rainforest inland. It has just the variety in vegetation for you to take up very many activities. At the beaches, you can join the local fishermen and learn how to fish or take a hike inland and enjoy the rolling landscape from the hills and mountains. There is literally something for everyone.
This is the largest island in Comoros, and is one if the perfect places for lovers to visit. It literally has something of everything.
The locals reside in the western parts of the island but to the south, there are the vanilla, coconut, banana and cassava plantation.
At this very same island, you could enjoy the local cuisine of the locals and most of the foods they enjoy have a side of sea food. The shrimps are quite lovely. The beautiful beaches are occasionally interrupted by solidified lava bringing a contrast between the sandy beaches and the lava deposits.
This just make the islands that bit attractive.