Our apartment is in Les Houches which is about 5km from Chamonix. There is a good bus service and excellent parking. Chamonix town is always buzzing, whereas Les Houches is a quieter place. The village specifically caters for families and children, Our apartment has the unusual benefit of a large terrace, and also unusually for a place of this size is all on one level.
There are good bars and restaurants within a couple of minutes walk. The Kitsch Inn in is a great local bar, with good simple food, local live bands and even a small kids play area inside. Ask for Digby! The Ferme des Agapes does good traditional Savoyarde food. There is a tiny but excellent pizzeria underneath, and also Le Basilic for a slightly higher level of cuisine. Le Creposaure is a great name for a nice simple creperie!
There is a good small supermarket an easy ten minute walk away, and also in the same direction a selection of more bars and restaurants, and the super-helpful Tourist Office.
I'll describe the winter activities and facilities separately, here are some ideas for summer:
There is an indoor climbing centre in Les Houches, and an outdoor practice wall in Chamonix (Les Gaillands). Experienced climbers should go to the Compagnie des Guides.
Dog sledding, snow shoeing, sledging are all available in winter.
In summer the main lifts are open and there is a near-infinity of high and low level hiking on well-signed paths. There is a kids amusement area in Chamonix - try the summer Luge - and also a swimming pool, gym and ice rink.
Whitewater rafting is available (the best is actually over on the Italian side). In the valley at Passy the Lacs du Passy is a huge (1 mile long) swimming lake with shade trees, a beach, barbecue pits, ice cream stands a a view of Mont Blanc.
Also in this direction there is a big thermal bath complex at Le Fayet.
There are two mountain railways, and the valley railway line goes to Martigny in Switzerland which has a world-class art gallery.