Summer: chill out by or in the lake, or explore the Old Town.
Winter: escape to the hills for ski & boarding in Europe's best resorts - all of them within 1-3 hours' drive.
Definitely skiing in winter either in France (La Clusaz, pays du reblochon) or in Switzerland (anywhere in Valais or Vaud but Verbier). During Summer either at the Bains des Paquis, Tropical (Windsurf club), or if you can on a boat.
Sad but true: use Geneva's location to get out of town..
are all enticingly close and offer highly diverse entertainment....
Lyon, Aix les Bains, Evian-les-Bains, and the ilk are close if you need to hike up a mountain or write music by a lake for a bit.