The historic centre is compact and best explored on foot. Almost everything worth seeing is within 15 minutes' walk of the Plaza de Armas. Ubers are widely available and cheap for getting to the bus terminal or outlying attractions. The city also has an extensive local bus network, useful for reaching the market areas east of centre, though routes can be hard to follow without local knowledge.
Renting a car makes sense if you plan to explore the surrounding area — Patzcuaro, Tzintzuntzan, the Monarch Butterfly reserve, or the copper town of Santa Clara del Cobre are all easy day trips.