To fully experience Joshua Tree, it is recommended to rent a car for the day. Car rentals start at around $50 per day for a small sedan. The drive from the airport to Joshua Tree is about 2 hours.
If you have more time, consider visiting other hiking trails in the park or taking a guided tour of the area. If you have less time, skip the Integratron or Pappy & Harriet's and explore more of Joshua Tree National Park.
The closest airport to Joshua Tree is Palm Springs International Airport (PSP) located about 45 minutes away by car. PSP serves several airlines including American, Delta, and United. Los Angeles International Airport (LAX) is also an option at about a 2.5-hour drive from Joshua Tree.