The park protects a very nice piece of rainforest. At Taveuni we stayed at the Maravu Plantation that was very pleasant but overpriced. We had been led to believe that the people here knew something about birding. It turns out they had no idea but thought that bullshitting us would be a good way around the problem. I would recommend the Garden Island Resort over any of the other establishments on the island.
Camping is another option.
I would recommend visiting the falls first and trying to get hold of him. Alternatively, if you have more time you can walk, but this will probably make you too late to find the Silktail. The track is in very poor condition, so good walking boots are necessary. We saw nothing new here, but there have been sightings of Shy Ground-Dove, and it is some of the best forest we saw. Kadavu is the fourth largest island in the Fiji archipelago and lies 90-odd kilometres south of Suva, rather more isolated from the main islands leading to a slightly higher degree of endemicity.