The Vail Valley is served by two airports, Denver International(DEN) and Eagle Regional(EGE).
Both are great airports and given Denver's size, it's an easy place to navigate. Weather and traffic will always be the X factor. Either way, worst case you will always get to your destination. Personally, we always fly into Denver.
Directions from I-70...
Next... exit N.Frontage Rd right to Red Sandstone Rd.
Arrival Area... "A" Building
Airport Arrival -Do I need to rent a car ?
Both airports have excellent shuttle options to the area. The shuttles will offer door to door service at a reasonable price.
If you plan on staying in the Vail area and only skiing at Vail or Beaver Creek, the bus system is great. Our place is better suited for Vail, as getting to Beaver Creek will take longer, requiring a transfer from the Vail Transportation Center. But it is possible. Uber and Lyft are also available but not to the availability you may be used to.
Doing without a vehicle is a much easier option if it's a small group. Larger groups will have to deal with a lot more moving parts which could make this a stressful proposition. If using a shuttle, be sure to call early to ensure you get preferred times to line up with your flights.