The nearest and easiest airport to travel from is the Phoenix Sky Harbor International Airport.
The Tempe Mission Palms offers a free shuttle service to and from Phoenix Sky Harbor International Airport. For more information, please visit their FAQ.
The PHX Sky Train is a free shuttle accessible from Terminals 3 and 4, which runs 24 hours/day and will take you directly to the 44th Street/Washington Metro Light Rail Stop. Metro Light Rail tickets are available ($2 USD for a one-way ticket, $4 USD for the day) at the stop. From there, take the eastbound train to the Veterans Way/College Ave station.The Tempe Mission Palms is about a five minute walk from there. All Valley Metro services are wheelchair and scooter accessible. Please be aware the Metro Light Rail only runs from 4:40 AM to 11:00 PM Arizona Time. For additional questions or a train schedule, please contact Valley Metro, via their website or by phone: (602) 253-5000 or TTY (602) 251-2039.
Additionally, on-demand rideshare services are plentiful here. Both Lyft and Uber have Wheelchair accessible vehicles available by request, as well as drivers trained to assist. You can estimate costs using ride.guru - though base fare from Sky Harbor to Tempe Mission Palms is approximately $12 USD, barring surge pricing.