It depends what kind of trip you wish to do.
Torino is only a 3 hours drive from GVA, and it's an interesting and elegant city to visit. If you drive a little southern, you will find Linguria and the seaside, Cinque Terre is known to be a little paradise and a must see. If you wish to eat good food and drink good wine, you might want to visit Langhe (South Piedmont) like Alba and sorroundings, the hills are beautiful and you would have the chance to visit where the famous for Barolo is produced, as well as other red wines. Also, there you would get to know the typical piedmontese cousine, which is totally different from the world-famous italian one. I'm sure you will enjoy.
I hope this gives you few ideas.
Cheers,
R.
