Visit the Chamonix Museums: all info about Museums 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 of 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.