There are huge variety of walks near chalet ranging from a stroll along the road to Saint Nicolas to a tough scramble to the Mont Charvin or Mont Pourri at the top of the Aravis ridge. You'll need the IGN 3531OT Megeve-Aravis walking map (available in the Flumet souvenir shop and the Arly Intermarche).
Right out of the chalet, you can walk as far as you like in the Aravis without encountering any but the smallest of roads. There are no ski lifts on this side of the valley. But this the alps, the altitude gain can be bigger than you expect so before you set out, check the altitude gain on the map! The height gain from the bottom of the valley to the top of the Aravis is well over 1000m and is a long all-day walk for a fit adult. A more moderate, but still challenging walk would be about 700m. Don't expect children to walk this far. A good half-day walk for an active group (including older children) is about 200 or 300m height gain. This is best achieved by driving up for a bit so that the walk starts in woods or meadows and then comes out on top. Alternatively you can take a chairlift on the other side of the valley - unlike many resorts generally the lifts are spaced quite far apart so its still very attractive to walk.
Le Treu and La Croix Cartier are two beautiful walks above the chalet. For le Treu, drive up past Saint Nicolas (signposted Chaucisse initially, but turning left shortly before Chaucisse) to les Avenieres. Follow the marked path from the cafe all the way to the top for a stunning 360 degree panorama over The Aravis, Mont Blanc, and the Baufortain. For La Croix Cartier, take the same roads all the way to Plan Chaucisse and follow the path towards the woods. When you're almost at the top there is a turn-off to the right that takes you up to the cross. Follow back to the main path and carry to return by a a path along the top that takes you down to a long track. There's also the option to make a detour nearer to the Aravis ridge if you're feeling energetic. Back at Chaucise, there's a lovely little bar under the Mairie in the former schoolroom.
Further afield, the Beaufortain valley beyond les Saisies is very quiet, or you can take the chairlift at Praz (open two days a week; check at the tourist office) to the Cret du Midi.
Nearer the chalet, the walk along the road to Saint Nicolas is lovely (turn left 50 m down the road, just below the Chateau, and carry on up) and you'll often see Chamois near the woods. You can also start on this road and take the footpath down to the lake after 500m, then turn left at the bottom of the hill and follow the river up on the opposite bank, up along the gorge through the woods. This will eventually winds up Chaucisse.