In reply to TomHall2016:
Other than spending all your money in the pub, it would be worth checking out routes accessible from the Torino hut on the Italian side of the Mont Blanc Massif, this can be accessed from Entreves just up the road from Courmayeur.
Mountaineering routes on the Aiguille d'Entreves & Aiguille Marbrees might be a good option, if conditions are right. Being February, you will most likely need skis to cross the Glaciers, however you might be able to get away with snowshoes for routes within short proximity of the hut / lift station.
On the Chamonix side, via the Aiguille du Midi, it might be possible to do a traverse of the Arete des Cosmiques, this had a major rock fall back in the summer, effecting the route, I have heard its being done now despite this, I would double check though. Again, you would probably want skis or snowshoes.
Post edited at 13:30