Courmayeur's immediate neighbour, La Palud is smaller and equally pretty if not prettier. It however, is extremely popular because it is home to the Funivie Monte Bianco, or the Mont Blanc Cable Car which climbs three quarters of the way up Western Europe's highest mountain and then heads into the town of Chamonix in France. Your first stop on this beautiful ride is Pavillion Du Mont Frety followed by Punta Helbronner. If you decide to continue on this spectacular interglacial experience, you will go into Aiguile Du Midi in France and then finally go down to Chamonix. Expect unparalleled views and weather that demands exceptionally warm clothes and sunglasses. The cable car departs every 20 minutes (8:30 am to 12:30 pm and 2pm to 4pm) and the tickets should cost you about 18 Euros. If you are not into skiing, this is probably the only thing you can do in and around Courmayeur but do check the weather conditions in advance. The folks at the tourist information office at Courmayeur Centre should be able to help you.
A free bus service runs every 15 minutes from Courmayeur centre and gets you to La Palud in about 7 minutes. There's a nice, albeit overpriced, authentic Italian restaurant opposite the bus stop in La Palud.