I have traveled to Cebu quite frequently but the visits were purely business in nature. A recent personal trip allowed me & my wife to check out the historical sites within Cebu City and the Basilica del Sto. Nino had been a must stop. The Basilica is located across the Magellan Cross and both sites readily gives you a vibe on how Christianity/Catholicism had started in the country (Philippines).
It would be good to go to the Casa Gorordo Museum before visiting the Basilica. The museum tour includes a quick AVP on the history of Cebu & the significance of the Basilica in the evolution of the city and the province.