Tombstone has no commercial air service and no train or bus connections worth considering. You need a car.
From Tucson: The most common approach. Take I-10 east to Highway 80 south (exit 302 at Benson), then follow Highway 80 about 25 miles south to Tombstone. The drive takes about 70 minutes and passes through classic Sonoran Desert landscape. Highway 80 is the main road through town.
From Bisbee: 25 miles south on Highway 80. About 30 minutes. Bisbee is an excellent complement to Tombstone — a former copper mining town with a completely different character (artsy, historic, with excellent restaurants). The two make a natural pairing for an overnight trip.
From Sierra Vista: 30 miles via Highway 90 north to the Highway 80 junction, then east. About 40 minutes.
Parking: Free parking is available along most streets in the historic district and in a large lot on Toughnut Street. On busy weekends the central lots fill up, but there is always parking within a short walk. The entire historic district is small enough to walk once you've parked.
Tombstone Municipal Airport, southeast of town, handles private aircraft only. There is no car rental at the airport.