Keep in mind that it's not easy to figure out how to ride a bicycle any distance in the region of Geneva without running into significant hills. Which might influence your selection of bicycle.
If you enjoy climbing up hills (I do, even on a train-station-rental bike), great. Otherwise you might want to look for clever combinations of train-bus with bike, so you can do more of your cycling in the downhill direction. (some of the Post-Bus vehicles in mountain areas of Switzerland have bike racks on the back of the bus There's at least one paper map you can buy which indicates which roads or paths are better for bicycling, and indicates where they have significant hilliness.
To ride longer distances on mostly flat terrain, could take train-bus to the Rhone valley between Martigny and the east end (opposite from Geneva) of Lac Leman, where the Chateau de Chillon restored castle provides a great non-cycling reason for a visit. (A tourist-visit city closer to Geneva is Lausanne: but other than the waterfront, it's rather hilly.)
Note that most of the land area surrounding Geneva is in France. One famous tourist place nearby in France is Annecy -- smaller but prettier city than Geneva, at the end of a smaller but prettier lake. There is a gentle/flat bike trail alongside above the southwest side of the lake, with prettier views than most bike trails, which could be ridden out-and-back -- or included in a 25-mile loop on roads around the whole lake (with 2 or 3 significant hills), which I've gladly come back to ride again a couple of times so far.
Rental -- I've rented bikes from two different shops near the Annecy bike trail, and both also had fancier bikes available - (one time Sharon + I rented a tandem and rode it together around the lake). So another option for a tourist day is to take the train from Geneva to Annecy and rent a bike when you get there.
Last edited by Ken Roberts; 06-06-10 at 03:54 PM.