Khorog (a.k.a Horog, Khoroq, Khorogh, Khorugh, or Xoroq) is the capital of the Gorno-Badakhshan autonomous region. Tourism infrastructure is well developed there and you can find a decent hotel, again in comparison to other destinations of the Pamir Highway. It has some of the highest concentration of hotels in the Pamir Highway area, though a distant city offers mainly two star accommodation.
