For the camels, the opening days, usually the 17th to the 20th. The herds are largest then, the trading is real rather than staged, and the dunes west of the ground are full of tents, cooking fires and animals; in previous years many herders have sold and gone by the 22nd. For the spectacle, the middle of the week, usually the 21st to the 23rd, when the tourism programme runs on the stadium ground and the balloons go up at dawn. For the pilgrimage, the 24th, Kartik Purnima, when the lake is the centre of everything.
Three nights covering the 20th to the 23rd is the compromise most first-time visitors are happiest with: the last of the herds, the whole programme, and the town before the Purnima crowd arrives. If you want the dip, come on the 22nd and stay through the 24th.