Loads of places because Geneva is connected to the Swiss rail system .... think Berne, Basel, Interlaken, Zurich, Lugano ............... go up the mountains - Pilatus and Rigi in Lucerne, Titlis in Engelberg, Jungfraujoch near Interlaken, also take the train to France eg visit to Annecy, and down into Italy from Lugano ... Lake Maggiore, Lake Como, Milan ...

You might investigate a European rail pass or a Swiss Travel Card or Half Price ticket if you decide to go rail mad ... and of course there's the classic Swiss train routes like the Glacier Express ...........

OH and you could always look at the low cost flight carrier Easyjet which flies out of Geneva to many different European countries BUT ... read the terms and conditions very carefully and respect the baggage regulations!