In reply to Alistair:
Most sightseers would be fine going up the Midi as long as they do not exert themselves too much, different story for an unacclimatised walker / climber intending walking out from the station to do a mountain route. However, as has been stated, a small number of people can be affected. So being aware and keeping an eye on each other is important.
A suggested plan if you are hill walkers that don't want to expend too much effort that my children enjoyed ( youngest was about 7 at the time but obviously all children are different) :
-Spend a day or so in the valley - great family cycling with bike hire. Ropes courses around the valley, great rock climbing instruction for kids at Gaillands, luges, mountain zoo down the valley, try a burger at Poco Loco in town.
-There are fantastic walks in the Aiguilles Rouges with awesome views of the main Mont Blanc Massif. For example take the Flegere / Index lift ( 2,300 metres ) and there is a lovely walk to Lac Blanc mostly downhill with a little up hill at the end. You can then walk downhill to the Flegere mid station and get the lift back down.
-The Brevent lift takes you a little higher with beautiful down hill walks and areas to explore. A favourite is watching or joining in with the parapenters at the halfway lift.
-For a real close up view take the Midi station lift to the half way point. From there a fairly horizontal and then downhill walk takes you to the Montenvers station where you can walk down or catch a train back down. Awesome views of glaciers and you are right under some mighty peaks.
-A lift system at the head of the valley, Le Tour, takes you to a steady uphill walk to the Albert Refuge with great close up glacier views and refreshments in the hut. You can walk on right to the edge of the glacier if you wish. There are other lovely walks around here too.
Just ensure you check the walking route conditions in the Office de Haute Montagne ( website info too ) because depending on the time you go ( I'm assuming summer ) and weather conditions there can be some snow patches on some walking routes that can be very icy / slippy in the mornings.
All these routes have options for a bit of boulder hopping, scrambling suitable for kids, lakes to dip feet in, opportunities to see Marmots, Ibex and eagles too.
The top Midi station, unless you are glacier equipped and experienced, is sightseeing only. A possible alternative adventure is to go through the tunnel and take the lift on the Italian side to the Torino Hut area. From there it is possible to get onto snow without being involved with crevasses.
Beware, alps and big mountains are seriously addictive! My son loved Chamonix when he first went aged 7, aged 17 he has climbed his first Himalayan peak...