Trains run just about every 15 mins to from the airport directly to Gare de Cornavin ( main train station ) when you leave the station head downhill on Rue de Mont Blanc toward the lake (Lac Leman) it is about four short blocks.
For the old city and most interesting sigt for a short visit head right crossing the bridge where the Rhone meets the edge of the lake, view the flower clock then head right uphill (past lots of upscale shops) towards the cathedral. I believe you can still climb the over 150 steps to the tower.
Also of interest in the general vicinity is an arcaded armoury.

If you love pork and especially pigs feet near the summit of Rue del Fountain there is a great little restaurant named "au pied de cochon"

mike