There are not that many sights to see in Cebu. The principal attraction of Cebu is the lifestyle and the atmosphere, not a wealth of historical sights. The sights we do have can be covered in half a day.
Most guidebooks or tourist guides will try to take you to the Taoist Temple and Casa Gorordo. Neither is worth a visit. The Taoist Temple is an unattractive, garish construction with nothing noteworthy or interesting to see, except perhaps the view - but a far better view can be had elsewhere, namely Tops or the neighboring Mountainview Park. Tops is a viewing platform in Busay, above the city. This photograph of Cebu City was taken there. Tops is open 24 hrs and is a favorite place for kids to hang out and get drunk at night. Mountainview Park has an entrance fee of 40 pesos, cheaper by 10 pesos; it is right below Tops. Both are reached via the Trans-Central Highway (see the Highlands) and are about 25 minutes from the city.
Now, while I do not recommend wasting time on the Taoist Temple for touristy purposes, if you are contemplating settling in Cebu, you may want to see one of the premier gated communities, Beverly Hills, and going to Taoist Temple would be the perfect excuse to get in - it's located right in the middle of the subdivision.
Casa Gorordo, meanwhile, is a museum of sorts; a typical house of Spanish nobility from days gone by has been preserved and restored for you to see. Owned by the Aboitiz Foundation, in turn owned by the powerful Aboitiz clan, Casa Gorordo has been designated a National Historical Landmark. Various antique artifacts are displayed in the rooms, but anyone who has been to Europe to see a real museum, or a preserved mansion for that matter, will be severely disappointed. You'd better skip it.
Cebu has a better museum, namely the University of San Carlos Museum, of Philippine history. While some of the exhibits resemble high school science fair projects, one does get a good sense of what life in the Philippines was like prior to modern times. One also learns that tribal cultures in ancient Cebu practiced two fascinating rituals. Now, if I revealed both, it would be like disclosing the hidden twist in a book you haven't read, so I'll tell you about just one. It's a bit gruesome. They'd file their teeth flat, bore holes, and insert little gold pegs - as shown in the photo at the bottom of this page - so that, whenever the person would talk or smile, you'd be eyeballing his or her dental decorations. Why would anyone go to such extreme lengths? Well, if you live in Cebu, it sort of makes sense. Sort of. See, this practice indicates that the ancient Cebuanos probably decorated every inch of their visible selves - their headgear, their clothes, their skin, and so forth - and, having ran of space, went for the teeth. This is somewhat reminiscent of the way modern Cebuanos decorate every square inch of their jeepneys.
Another attraction you may want to see is Magellan's Cross, on Borromeo street, right across City Hall. The great Portuguese seafarer and conquistador brought Christianity to Cebu, and planted a cross. This cross is - get this - represented by a replica which is further encased in wood, which is available for public viewing inside a purpose built hut. This is because devout believers would often make off with bits off the cross, valued as relics. The cross is important because of the symbolism. Magellan's Cross marks the incursion of Christianity into Asia, and symbolizes the advent of Western religion and principles on these islands. Magellan's Cross is a worthy destination not because the cross looks particularly interesting - it doesn't - but because it is the marker of an event which heralded the formation of the only Catholic nation in Asia.
Right next to the little hut housing Magellan's Cross is the Church of Saint Augustin, better known as the Basilica del Santo Nio. This is no less than the soul of Cebu. One can't even begin to discuss Cebu without first considering the Santo Nio, Cebu's holiest of holies, so important to the psyche of not just this island, but the entire country. This actual Santo Nio is found inside the Basilica del Santo Nio, also known as Saint Augustin Church. You can get quite close and take a good look, as long as a mass is not ongoing. In the photo on this page, the Santo Nio is in right in the middle, above the crucifix. [MORE ABOUT THE SANTO NIO]
It is rather ironic and perhaps appropriate that Lapu-Lapu is also an object of devotion, second only to the Santo Nio in the hearts and minds of Cebuanos. Lapu-Lapu was a chieftan in Mactan who, unlike Rajah Humabon, was not enthralled by the idea of converting to Christianity, and who consequently ended Magellan's global voyage by killing him in hand-to-hand combat. The site of Magellan's demise, in Mactan, is commemorated by the Mactan Shrine, also known as Magellan's Marker. Right next to it is a statue of he-man Lapu-Lapu, muscles rippling and brandishing his sword.
Located next to Plaza Independencia is the Fort of San Pedro. This was a Spanish Fort, a Guantanamo of sorts where Cebuano insurgents were imprisoned by the occupying Spanish forces. Then it passed into the hands of the Americans, who used it as a barracks, until the Japanese took over. Parts of the fort have been restored. The fort used to house a small museum, but that is now closed. San Pedro still remains a pleasant destination, however, especially if the weather is nice.
A stone's throw from San Pedro is Carbon Market, which is definitely worth a visit, but this is covered under Shopping.
Last but not least, I recommend a visit to the Butterfly Sanctuary. This used to be the home of Cebuano lepidopterist Julian Jumalon, who must have been quite an amazing character until he passed away. There are three reasons you should visit the Butterfly Sanctuary. First, you can see the plants that butterflies like, and live butterflies fluttering about. The live butterflies themselves are not that stunning, but finding about their habits from the guide is rather interesting. Second, Professor Jumalon amassed a vast collection of butterflies from all over the world, by trading native Cebuano butterflies for African, Papuan and other butterflies. Third, he used the wings of dead butterflies to make mosaics These look like fairly accomplished paintings, at first glance, but they are actually far more than that; the wings change color according to the light. The mosaics are delicate; photography is strictly prohibited in the museum exhibiting Professor Jumalon's works.
If you have young kids, you may fancy a visit to Crocolandia, a crocodile park aimed primarily at locals. In addition to crocodiles, they have a wide range of wild animals in captivity, including an ostrich and a tarsier, which I'm pretty sure is illegal. Personally, I despise the place.
Lastly, you may wish to pay a tribute to the heroes of Philippine history by dropping by the Heritage Monument in Parian. And that just about wraps up a sightseeing tour of Cebu.