The centre is walkable — almost everything within the old town is within a fifteen-minute walk of the Jardín de la Unión. Be prepared for steep alleys and many stairs; comfortable shoes are essential.
The outlying sights (La Valenciana, the Mummy Museum, Cristo Rey) are best reached by taxi. Local buses run from the bus station and the Mercado Hidalgo but the routes are not obvious to visitors. Taxis are inexpensive; fares within the city are usually fixed. Uber and Didi both operate.
The underground tunnel system runs beneath the city and is the only way for cars to move around the centre — it can be confusing, but taxi drivers know it intimately.