are shuttles buses available from leysin to gstaad ski resort and ski resorts inbetween. also from leysin to ski resorts less than 30 miles to the northwest and southwest of gstaad.
You can go from Leysin to Gstaad by public transport, but this is slow (about 2 hours) and complicated. You can hire a car, but this will also be rather slow. Remember that hese are the alps, and it is winter. Anyway, www.sbb.ch is the site to inform you about the totality of public transport available in Switzerland.
As suggested by K_V_B, www.sbb.ch is the site to find out about public transport travel times etc.
There is a regular bus freom Gstaad to the Ski resort of Glacier 3000 at Les Diablerets. This takes just under an hour. Of course, there is also plenty of skiing around Gstaad itself, as are there good options accessible by train at Adelboden and Zweisimmen.
Travelling by car between Gstaad and Leysin takes about 40 minutes in good conditions. The roads here are well cared for in winter, so you should be able to make the journey trouble free, most-likely without chains, but it will take about half the time again.
If accommodation prices in Gstaad are what is putting you off, I can recommend the Gstaaderhof Hotel. Been many times. Still not dirt cheap, but reasonable, and great, comfy rooms, with good breakfast.
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Address: Bernese Oberland, Gstaad, Bernese Oberland, CH - 3780, Switzerland