Train: By far the best option, the Regional Transportation District (RTD) runs a convenient and cheap train from Denver International Airport to Union Station in downtown Denver, about one mile from the hotel. The fare is a paltry $9.
At DIA, the station is located at the far southern end of the main concourse (where ticketing and security are located), UNDER the Westin Hotel. Purchase a one-way or round-trip ticket at the vending machines; conductors WILL check your ticket on the train. It takes ca. 35 minutes one way, and the train runs every 15 minutes. More information can be found here. Once you arrive at Union Station, you have several options:
Car: Uber, Lyft, and taxis all serve Denver International Airport. During off-peak hours Uber and Lyft fares should range between $35 and $50; Taxis will be closer to $75.
Rental Cars: All car rental facilities are located off the main airport; you have to catch company-specific shuttle busses to the rental counters about two miles away. NOTE: The meeting hotel does not have a free parking lot. You can park on the street or use their valet parking at $39/day.
If you drive: parking at the Museum is free, but this is one of our busiest weeks of the year, so parking at the Museum will be tough particularly later in the day.