Palm Springs International Airport: The sensible airport for Indio. Take a pre-booked car, rideshare, or taxi directly to your hotel: roughly 30 minutes and about $50 by taxi in normal conditions. Public transit exists in the valley but is too slow and transfer-heavy for most arrivals, especially with luggage or during festival weekends.
Ontario International Airport: Useful when fares or flight schedules beat PSP, but only if you will rent a car. There is no public-transport link to Indio; the drive is roughly 1½ hours without serious I-10 traffic. A one-way rideshare is expensive enough that a rental usually makes more sense.
Imperial County Airport, El Centro: A limited-flight fallback, mainly for Los Angeles and Phoenix connections. There is no public transport onward to Indio, so arrange a rental car or private pickup; it is not a practical choice unless the flight is unusually convenient.
Indio long-distance bus stop / Hwy 111 & Flower Transit Center: Greyhound, Cruceros and some other intercity services use Indio, while FlixBus uses the SunLine stop at Highway 111 and Flower/Golf Center Parkway. This is the practical arrival point if coming overland from Los Angeles, Phoenix, Las Vegas, or San Bernardino; use SunLine or a short rideshare for the final leg to your accommodation. There is no passenger-rail station in Indio.