I'm sorry, but there seems to be some confusion in your question. Cebu City is not in Singapore; it is located in the Philippines. Nevertheless, if you are in Cebu City and interested in visiting museums, I would recommend checking out the Museo Sugbo or the Casa Gorordo Museum. If you are looking for similar types of museums nearby, you might also want to consider visiting the Yap-Sandiego Ancestral House or the Jesuit House Museum.
I apologize for any confusion, but Cebu City is actually located in the Philippines, not Singapore. That being said, some popular local dishes to try in Cebu City include:
1. Lechon - roasted pig served with liver sauce and vinegar
2. Sinigang - a sour soup made with pork, shrimp or fish, tamarind, and vegetables
3. Adobo - a dish of meat (usually chicken or pork) cooked in soy sauce, vinegar, garlic, and other spices
4. Chicharon - deep-fried pork skin or rind
5. Puso - rice wrapped in woven coconut leaves, also known as "hanging rice"
There are many other delicious dishes to try in Cebu City, but these are just a few examples of some of the most popular and typical options.
I apologize for the confusion again, but Cebu City is still in the Philippines and not in Singapore. As for fun activities that locals enjoy in Cebu City, here are some suggestions:
1. Visit the famous Magellan's Cross and nearby historical landmarks
2. Go on a food trip to local markets and street food stalls such as Carbon Market and Larsian BBQ
3. Head to the beach in Mactan Island for water activities such as snorkeling and island hopping
4. Attend Sinulog Festival (held every January) to experience the city's biggest and most colorful celebration
5. Explore Osmeña Peak, the highest point in Cebu, and enjoy trekking or hiking with scenic views.