Yes! You can take an easy scenic walk into the centre of town within 40mins from the hotel or you can catch a 5-10min public bus every 30min from the just outside the hotel entrance. There is also a mountain train that goes directly to the town centre from just in front of the hotel too every hour or so. The public transport is highly reliable and we would recommend over a rental car, plus you get a free pass from the hotel on arrival.
Transport timetables can be found here: https://www.chamonix.com/infos-et-services/transports/se-deplacer