Hilton Santa Fe Historic Plaza, Santa Fe, New Mexico
Flying to Albuquerque (ABQ) and renting a car works and is indeed the standard approach. ABQ to Santa Fe takes about an hour.
Another option for this meeting is driving down from Denver, but there's a dropoff fee for most rental cars. Driving time from Denver to Santa Fe is 390 mi, 5 hours 42 mins on I-25 (Google Maps) and about the same by more scenic roads.
There's a shuttle from ABQ to the major hotels, including the Hilton. One Way $28 Per Person, Round Trip $48 Per Person
There's also the possibility of taking the brand new light rail, the Railrunner. It has a good schedule weekdays and pretty sparse weekends. You take a bus from the airport to the train station and then get let off at the Railyard, probably 5-6 blocks from the hotel. It's cheap (~$6) and fun for train buffs.
Santa Fe does have an airport with just a few flights per day. Its airline is American Eagle and it does have flights from Denver. Sometimes the price is more-or-less comparable to going via ABQ and sometimes it's expensive.