First off, do not go on a helicopter ride inna Third World nation unless the letters UN are painted on the side or there are guys in OD green jumpsuits with US Army stitched on the breast pocket and are carrying large caliber guns. Helo operators even in this country are notoriously lax in their training, maintenance, and hiring procedures, so you can only imagine what it's like in a place where there are no rules.
Ok, the beaches of Belize can be very secluded, romantic, and amazingly inexpensive as long as you are willing to travel to get to them. For about $50-75 a day you can have a very nice bungalow with full maid service, all the fresh fruit, fish, and alcohol you can consume on your own private beach for as many people you will see.
I've heard Costa Rica is a terrific place to go as well-- very American oriented in terms of what they offer for lodging, food, services, entertainment, etc. It's supposed to be very cheap as well, but not as much as Belize. Good tropical atmosphere, jungles to explore, mountainous regions as well.
A Barefoot cruise that sails for 7 to 14 days in the Caribbean is reputed to be phenominal if you don't mind a boat rocking and no more than 100 passengers (some boats have fewer than 20). They go to lesser populated ports of call and are much more personal. This is what Mrs. Totem and I will be doing the next time we take a cruise. These are slightly more expensive than a standard cruise.
On the same note, there is a new mega-large ship that goes out of Florida with the Royal Caribbean cruise line. It's the largest boat in the world, or so they say. Tons of stuff to do, large cabins, and losts of island hopping.
I was going to suggest a longer trip, but you said 6 hours was your max, so my suggestion of trying northern Japan is most likely out of the question. Avoid Tokyo unless you can take large crowds. However, there's nothing like the Far East for exotic. Hong Kong is a wonderful destination too.
Totem