Mesa is car-dependent for most of its area, but downtown is a partial exception. The Valley Metro Light Rail runs east-west through central Mesa, connecting downtown Mesa to Tempe and Phoenix with regular service. This makes it genuinely practical to get from Mesa to Sky Harbor Airport, Tempe's Mill Avenue, or downtown Phoenix without driving.
Within Mesa itself, the distances between attractions are large enough that a car is almost always more convenient. Uber and Lyft are widely available. Rental cars from Sky Harbor Airport or local agencies are the default for visitors covering multiple sites.
For Usery Mountain Regional Park and the Commemorative Air Force Museum at Falcon Field, a car is essentially required. The park is accessible via Usery Pass Road off McKellips; the museum is at 2017 N Greenfield Road in Mesa's eastern suburbs.