Air-conditioned MyBus is useful for some city journeys. Services connect the airport, SM City mall, SM Seaside City Cebu and the North Bus Station; trips cost P25 and buses run 6am to 10pm. MyBus only accepts cash from the airport and SM City mall. Otherwise you have to purchase a travel card (P200, which is preloaded with P100 credit); these cards are available from booths.
Few travellers bother with them but jeepneys can be useful for short hops (P7) along major boulevards and to get to major landmarks (just read the placard). From Jeepney Terminal Ayala (also known as PUJ Ayala) you can catch a ride to destinations including Lahug and Lapu-Lapu City; jeepney 14D is very useful as it passes along N Escario St, Pres Osmeña Blvd and Fuente Osmeña circle to Junquera St (where the Southern van terminal is located).
Taxis are the easiest option for getting around the city. Grab, Uber and Easy all operate in the city. Standard city taxis are usually as cheap as app-based taxi services, easy to catch and will almost always turn their meter on. Flagfall is P40 and then P3.50 for each additional 500m (or two minutes waiting time).