You can drive around the mountain. It goes through the Mont Blanc tunnel and Aosta and over the St Bernard pass.
The best option is to use a tour bus starting at Chamonix train station. As of 2009, it is about 47 Euros. Considering how much distance it covers, it is a bargain. Just going through the tunnel is a lot; may be 35 e in 2009 per person.
It is called "Tour du Mont Blanc". It leaves from Chamonix at 9 am and returns at 18:15. You could possibly ask them to let you off near Finahut. It does not hurt to ask.
Food in Aosta is great. Dine there and wine is also good.