I'll add to the Costa Rica recommendations, specifically the Pacuare Lodge. It is not the beach, it is in the rain forest along the Pacuare River. You raft in and out. Even if you drive in w/ 4x4s (if the river is too high) the only way into the actual place is across the river via a gondola. Very remote, no power to the cabins, very natural. Check out their website and read about it. If you go, spring for the honeymoon suite called the Jaguar iirc because it has a propane heater that gives you hot water even if it is cloudy (the other cabins are on solar). The place is amazing, surrounded by birds and wildlife all the time, and the food is remarkable considering everything comes in by raft.
You shouldn't stay more than 3 nights there. Work it into a longer trip to other parts like Arenal, the beach, etc.