The chalet is perfectly located to try different resorts. As it doesn't cost much more to buy six daily passes than a weekly pass, if you're not tied down to one place by lessons you can get up each morning and ski wherever you fancy. Here are some suggestions:
La Giettaz (20 min) Drive halfway up the Aravis pass to the village of Giettaz, turn right as you come out of the village, the ski area is 1 mile further on (the road is not steep and is kept open in winter). From the top of the lift you can connect through quiet runs to the Jaillet area of Megeve and on to Combloux, a huge distance. This is a special and beautiful outing. Make sure it's not too windy or they may close the connecting lifts. Included on the Megeve lift pass, or it also has its own (cheaper) pass ("Portes du Mont Blanc").
Les Grands Montets at Argentiere (just under 1 hour): This is the most famous run in the Chamonix valley and is a must for good skiers (not ideal for beginners). It's high so generally has good snow cover. Drive past Megeve and follow signs to Chamonix, once you're in the Chamonix valley Argentiere is a little way past the town of Chamonix). If you were actually staying in Chamonix, it would take you nearly that long to get there on the crowded shuttle buses. Argentiere is very popular so leave early in the morning to avoid the queues, and avoid weekends in peak periods. You can book your place on the upper section of the Grands Montets lift on the internet, when you buy your pass, or take your chances in the unreserved queue. The run from top is long and beautiful, but don't be scared by the hype: it's a moderate black run.
Chamonix: Chamonix (under 1 hour) is actually not a single resort but a long valley with several lift systems (Flegere, Brevent, Le Tour, Les Houches, Argentiere). They tend to be crowded compared to Megeve or closer lifts. The powder gets tracked out right away, unlike Megeve and Espace Diamant. However, on a quiet day, it's easy to get to Flegere or Le Tour and it won't take you much longer than if you were staying in the Chamonix valley anyway and relying on the buses. Also, you can take the charming Mont Blanc Tramway in Saint Gervais (30 min) directly up to ski at les Houches, without driving round into the Chamonix valley (as you approach Saint-Gervais from Megeve, turn left at the roundabout over the viaduct, then left at the end of the viaduct towards the station).
Courmayeur (1 hour 10 min) is lovely. It takes just over an hour if there's no traffic in the Mont Blanc tunnel (usually fine around 8 or 9 am; check on the web). Drive up towards Chamonix and before you get there follow signs to Italy. As you come down out of the tunnel there is a big lift and car park on the right hand side. You can start with a proper cup of coffee in the restaurant by the lift. Varied ski-ing and fantastic food. It's better to go on weekdays because the Milanese flock there at weekends.
Contamines (40 min): if you have a Megeve weekly pass, a day in les Contamines is included. As you approach Saint-Gervais from Megeve, turn right to les Contamines. Contamines is uncrowded with a more open feel than Megeve as it's above the tree line.
La Clusaz (20 min): drive over the Aravis pass - this is one of the only alpine passes that is kept open all winter. It's not steep or exposed to drive over. As you come down towards la Clusaz you can park by a small lift without going into the centre of town. La Clusaz doesn't offer anything better than the options above, but you can try it for variety.