Go to a Museum in Chamonix. The Alpine Museum in Chamonix is well worth a visit. You can also take a tour down in Switzerland and visit de Pierra Gianadda Foundation.
Visit also the Espace Tairraz or the Maison if Heritage in Chamonix Mont Blanc town.
There is also the Galerie du Globe in Argentiere as well as art exhibits in many of the hotels. Further afield, the Art Gallery in Martigny is excellent.