Yeah, you'd wanna be at the airport between 4:30 and 5am...

From where I live, I can usually take one of the first trains in the morning and make it to the airport for an early flight. Yverdon however's another ball game. If you end up doing an all nighter at an airport (never tried the Geneva airport... they may not even let you in?), you'll be truly and well exhausted by the time you get off your flight destination... The day will be spent sleeping or in a drowsy haze (which isn't that nice).

Try the Holiday inn or Crowne Plaza near the airport. They're walking distance from the airport entrance which would save you some $$$ on taxis, and you can get to them from the airport train station. Prices may not be too bad for a singe night.