Planty of stuff in Italy either in Piemonte or Liguria...but you need to do some research I am not an expert yet...
I am assuming you are talking about hiking...
In Chamonix without crampons you are limited to that...but you can rent boots, crampons and ice axe in town and go for some nice solo climbing on the high mountains...
But if you do not want want to rent gear your option is the Aiguille Rouge. There is a beautiful and engaging traverse that you can do from Le Brevent all the way to Lac Blanc and further, it involves some scrambling, ladder climbing, snowfield crossing and a lot of up and down. I think the time required is about 8 hrs, but I never done it...