The city centre is flat and manageable. The two keratons are about 1km apart and walkable from each other in reasonable weather, though the heat and humidity make long walks tiring. For short distances, becak (cycle rickshaws) are the traditional option and still common in the old town; agree on the fare before setting off. Ojek (motorcycle taxi) drivers are everywhere and faster for slightly longer trips.
Grab and Gojek both operate in Cirebon, which makes getting around straightforward if you have the apps installed. For the Gunung Jati tomb, 5km north of the centre, an ojek or online taxi is the most practical option — it is too far to walk comfortably.