Visited November, 2012. It is not an easy site to visit. It is not easy to mark precisely what was really inscribed as three parallel rivers. There are no good maps available in Yunnan. I have to do a lot of paperwork before going there and found out that the easiest way to visit one of the inscribed areas is to go to Shangri-La (former Zhongdian) and try to reach the site from there.

Shangri-La has its own charm (and it is good to stay there for some time, city is very interesting including old town, as well as surrounding countryside) and located nearby Podatso (Potatso or Pudacuo) National Park which is part of Haba Snow Mountains Area and one of the inscribed UNESCOs.

The park is 22 km from the town by good asphalted road. I am not sure about a public transport there but you can easily arrange a tour from Shangri-La or go there by bike (that I did). To get there it is about 2 hours (the road goes really through the mountains). Once you arrive at park entrance (visitors center) you should buy very expensive ticket to go through (in fact it was the most expensive entrance fee I have ever encounter in China - 190 Yuan).

For that price you get free bus transportation inside the park and the possibility of perform different treks inside. The most popular is around Shudu Lake (approx. 4 km, photo attached, google coordinates 27.905487, 99.948334) and on the banks of Bita Lake (similar distance, google coordinates 27.822645, 99.987970). Transportation between treks is assured by the same free bus. Another interesting place is Militang - huge meadow surrounded by small hills. The landscapes are amazing, be aware that you are located at the attitude over 3.500 meters above sea level, Militang is even higher at around 3700.

Other option to see the world heritage area around Shangri-La is to go to Balagezong Scenic Spot (National Park). It is located some 70-80 km north of the town, and there are daily tours the town (I found one agency offering tours for 50 Yuan per person but they required 3 person as a minimum)