Most visitors coming from Mexico City drive west on the toll highway toward Toluca and then south through the mountains into the Zitácuaro valley - the drive takes about 2.5 to 3 hours depending on traffic leaving the capital, and the mountain section is genuinely beautiful once you clear the Mexico City sprawl and start climbing. Direct buses also run from the TAPO terminal in Mexico City and take roughly similar time with less stress, which for a first visit is often the smarter option.
The nearest commercial airport is in Morelia, the state capital of Michoacán, sitting about 2 hours west of Zitácuaro by road. Car rental is available at Morelia airport and the drive east through the mountains is straightforward. Mexico City's airports are a further but more connected option for international arrivals, with the bus connection being simple enough that renting a car isn't always necessary.
Getting around Zitácuaro itself is mostly on foot from the hotel given the central location - the main plaza, market and most restaurants are walkable, and the historic center is compact enough that you rarely need transport for anything within the city itself. For the butterfly sanctuaries you'll need either a car or an organized tour, as public transport to the reserves is limited and the mountain roads require patience.
A car is genuinely useful for exploring the broader region - the hot springs at Ixtapan del Oro, smaller mountain villages, the various butterfly access points that are harder to reach by public transport. But for a stay focused on the hotel and the main sanctuary, a car is a convenience rather than a necessity, and the bus connection to Mexico City works well enough that many guests arrive without one.
Parking at the hotel is limited and the streets of the historic center are narrow - this is worth knowing in advance if you're arriving by car, because it will require either patience or a short walk from a nearby lot. Not a dealbreaker but worth planning for rather than discovering at 9pm with a full car after a long drive.