A car is absolutely essential in Kanab. There is no public transport and the attractions — Zion, Bryce Canyon, the Grand Canyon North Rim, Grand Staircase-Escalante — are all significant drives on roads that see little traffic outside summer. Rental cars are available at the St. George airport; it is worth arranging a vehicle before you arrive in Kanab.
Many of the dirt roads in the monument and the backcountry around the Paria require a high-clearance vehicle, and some require 4WD in wet conditions. The main highways (US-89, Utah-9) are all paved and fine for a regular car. In summer (June–August), fuel up whenever you have the opportunity — there are long stretches of US-89 with nothing between towns.