Denver International Airport (DIA) is the closest airport to Boulder.
DIA is serviced daily by most major airlines, and is a hub for United Airlines with non-stop flights from many major North American cities (https://www.flydenver.com/).
The distance from DIA to the University of Colorado Boulder is approximately 41 miles (66km). This will take approximately 40 minutes in a taxi, costing around $80-90.
You can find more information about transportation options here; https://www.flydenver.com/parking_transit