Hmmm. We have only stayed in Lanslevillard, both summer and winter, with 3 kids under 11.
Lanslebourg probably has the most concentrated collection of restaurants and bars but these extend along the main valley road. The accommodation is mostly located along this and the streets behind. The ski lifts are all located on the opposite side of the river so you would have to walk to the bridge. It is all flat however. There is a modern complex slightly further up the valley on the same side as the lifts which you can ski into but it is more remote from the main centre.
Lanslevillard is more hilly but is perhaps more centred around 3 main areas with further shops and bars along the main road.
Balcons (villages and le haut) are the furthest up the valley and are both modern purpose built accommodation. Both are within an easy walk of the new Le Haut gondola and the swimming pool, a supermarket and a few bars and restaurants. ESF and ESI ski schools both meet there.
There is the old town where we stay. It is a steep walk uphill from the shops and bars on the main road but has one restaurant and the essential food and gear shops. The accommodation is mostly traditional houses with a few purpose built apartment blocks. We stay on rue des Essarts and have a 50 foot walk to the piste and an easy slide down to the colomba chair lift where ESF also meet. There is lots of accommodation on the snow front in this area.
Finally there is purpose built accommodation around the old Vieux Moulin gondola. This also has some shops and restaurants but is some distance from the main shopping area, including the excellent boucherie and fromagerie. There is a free bus though. I think ESF meet there.
Personally we like the old town, we don't mind the steep walk down to the valley road and Essarts suits us with its rapid piste access and proximity to a boulangerie for breakfast. We tend to eat in at night.
Be aware that there are some modern accommodation complexes between the two villages which are luxurious but are a long way from all of the services and you would need to rely on the ski bus or a car.