There are two main routes for driving into Prescott.
There are two main airports a visitor to Prescott might fly into: Phoenix Sky Harbor International Airport (PHX) in Phoenix, and Ernest A. Love Field (PRC) in Prescott. Sky Harbor services most of the largest airlines and is located about 90 minutes from Prescott. Ernest A. Love Field is a much smaller airport, servicing only the Great Lakes Airlines with a limited flight schedule.
Having a vehicle might make reaching the outlying attractions easier, but if you intention is to take in the downtown Prescott area and the weather is right, getting by without a vehicle is absolutely feasible. Simply book a shuttle from the airport and a hotel close to downtown Prescott.