To the original question, you've already skied Chamonix, so you know the character of the Alps is quite a bit different than western US. balso's comments are spot on.
Zermatt is a world-class high mountain resort that is car free. Scale dwarf's anything in the US. Elevation is 5280 feet (mile high town). Three separate interconnected areas with up to 7000 ft of vertical, plus the ability to ski into Italy with another huge ski area (Cervinia).
Selva di Gardena, my favorite and also recommended by balso is also high at 5150 feet elevation. This is great for scenery and ski-touring. You can ski the "Sella Ronda", a 25 mile circuit around the Sella Massif, skiing village to village and end up back where you started. You can do it clockwise or counter-claockwise.
Kitzbuehel is a lower elevation at 2500 ft, so a little less snow-sure, but good snow-making. Interconnected with other surrounding ski areas.
Distances by train are about 8 3/4 hours Zermatt to Kitzbuehel. 3 1/2 hours Kitzbuehel to Bolzano, then a 1 hour bus ride to Selva. Bolzano to Zermatt is 7 1/4 hours.
If you wanted to rent a car, I would fly to Milan and rent there, then drive to Zermatt, then Kitzbuehel, then Selva, then return the car at Milan. Don't forget to purchase a Swiss vignette (toll sticker) and attach it when you enter Switzerland and the same for Austria.