The Nam Tok Thilawsu falls are near the headquarters of the Um Phang Wildlife Sanctuary, which is about 50km from Um Phang, towards Sangkhlaburi in Kanchanaburi Province. The wildlife sanctuary links with the Thung Yai Naresuan National Park and Huay Kha Kaeng Wildlife Sanctuary (another Unesco World Heritage site), as well as Khlong Lan and Mae Wong National Parks to form one of Thailand's largest wildlife corridors and one of the largest intact natural forests in Southeast Asia.
The 2km path between the headquarters and falls has been transformed into a self-guided nature tour, with the addition of well-conceived educational plaques. Surrounding the falls on both sides of the river are Thailand's thickest stands of natural forest, and the hiking in the vicinity of Nam Tok Thilawsu can be superb. The forest here is said to contain more than 1300 varieties of palm; giant bamboo and strangler figs are also commonplace.
You can camp at the sanctuary headquarters at any time of year, although it's best to book ahead from November to January when the falls are a particularly popular destination for Thais. This is also the only time of year when food is generally available at the headquarters; if you visit at any other time you'll have to bring your own.
Note that in recent years the access road to the sanctuary headquarters has been closed for part of the rainy season (June to September) to ease environmental damage. You can still visit the sanctuary and waterfall, but only by boat or trekking.