There is no single Chamonix piste outside the door of every hotel. The ski areas — Brévent–Flégère, Les Grands Montets at Argentière, Les Houches, Le Tour, and the Aiguille du Midi for the Vallée Blanche — are separate. Stay in the town if you want restaurants and a bus to more than one area. Stay in Argentière if the Grands Montets are the point. Stay in Les Houches if you want the gentler area and you accept the bus back.
Chamonix is not a 2030 competition venue. Do not pay a Games premium for a race that is not here. Geneva is the usual airport. The Mont Blanc tunnel is the road toward Courmayeur, which is Italy, not a French Alps base unless that is the trip you meant.
The Vallée Blanche is a glacier route. Hire a guide. A hotel booking does not include one.