I too would spend the night in Lyon. Perhaps at the Sofitel Bellecour or the Hilon on points. Enjoy a true haute cuisine dinner!

I've taken the train between Lyon and Geneve several times. Sometimes I take the TGV from Lyon to Bellegarde and then change to a regional. It's a very beautiful route in some places, especially around mid-day when the sun is high and can light up the mountain passes.