I think Bhutan was by far one of my most exotic trips. This is a small, landlocked country bounded by Tibet to the North and Northwest and the rest by India. To the East is the state of Arunachal Pradesh, to the South, Assam and West Bengal and to the West Sikkim. A range of high Himalayan peaks divides Bhutan and Tibet.
Bhutan was only opened for tourists in 1974 with the Paro airport opening in 1983. The government is allowing more tourists into the country who now must pay a minimum daily fee of $200 but going to $250 in 2012. This is actually quite a good deal as it includes your lodging, food and guide. They are trying to avoid as many backpackers as say Nepal.
As far as arranging your trip, I believe it is required to have a guide, if not then it is still good to have one particularly if you travel to the smaller towns in the center. Asia Transpacific Journeys had both group and private trips. Ask for Eric Kareus who is excellent. Country Walkers has a good program. I was unable to do their trip but I used their local operator and was very pleased with my private guide and driver.
One more thing, Druk Airways, the only carrier into Paro, offers flights from Bangkok, Kathmandu Nepal, Delhi and Calcutta India. You can also now fly from Singapore. The planes are generally small, though they did add two airbus jets, so make sure to book your flights early. I went in and out of Bangkok.