I've hiked it in 10 days in July three years ago, or was it four and really had a great time. Part of the fun was that it was a bit busy, a very international walk and I met loads and loads of people, all ages and sizes. I camped and found it so easy to find a good site and I also stayed in a couple of Refuges as well, the best being the Refuge Bonatti in Italy. Fantastic fun, the meal started at 7.00pm (about 100 people), all sober then but we were not for long! Singing, musicians, poetry, actors, all contributed to a great evening but I had hangover the next morning. I also wild camped behind some Refuges as well and paid to eat with the people staying there.
The best starting place, if starting from the Chamonix area, is also to walk the TMB anticlockwise. First, along an easy green footpath from the town centre (you can also catch a train or bus) and then start the hike proper at Les Houche. Very nice campsite about 150mts from the trail, lots of hotels and eating places. If you start at Les Houche, its a gradual up and down on the first day rather than a steep climb on the first day. If starting at Chamonix, you either have to catch a cable car to the top of a mountain and then start the trail, then followed by a steep downward plod to Les Houche, or to walk up the mountain to the trail (a long long slow plod, not so good if its blazing hot or its bad weather) and then still have to face face the downward plod to Les Houche. I personally found that hiking down to Les Houche on the last day was the best way for me to finish the walk.
Contamines has a lovely campsite (I ate my evening meal on a restaurant veranda overlooking a lake, beautiful!) and I had a free pitch at Les Chapieux and just loved Cormayeur. If you are now worn out and want to get back to Chamonix, just catch a bus through the Mont Blanc tunnel. I found the hardest decision to make was at Champex, to take the northern easier route or to take the harder Ferete d'Arpette route? I chose the northern route, it was a good choice, the views and the weather was perfect! I met an eccentric 80 year old Aussie in a Refuge en route at lunchtime. He did his 'walk' on a donkey and was totally in love with Prof. Alice Roberts, he wouldn't stop talking about her! I hiked over the Ferete 'd Arpette the following year when I attempted the Chamobix to Zermatt hike. It was really worth it!
Sorry to drone on but I really enjoyed every minute of this route!