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The closest airport to Boulder is Denver International Airport (DEN), which is approximately 45 miles from Boulder.
If you do not live near a hub airport, your best option for getting a non-stop flight to Denver is on United, Frontier, or Southwest airlines.
There are several options to get to Boulder from the airport:
Linked are driving directions for taking the E-470 Tollway ($8), or I-70 from the airport to the hotel. The tollroad is quicker and has less traffic than I-70. Most rental car companies have toll passes in their rental cars so toll charges will be paid through the rental agencies.