Chittagong Hill Tracts
You have to arrange permits! For each sub district of the Chittagong Hill Tracks if you are a foreigner. They will actually check you. You might receive a police escort (and need to pay for it), if you want to go outside the main cities. They fear you might otherwise be captured by rebels and used to influence the political process. This has actually happened with a group of Scandinavian engineers.
It is though actually a quite beautiful region. The Region would be ideal for hiking.
Rangamati has a nice lake. A trip to the water fall is nice (although the boats are a bit noisy).