Like any bustling metropolis, especially in less affluent countries, these cities have their safety concerns. Manila and Cebu share similar traits in this regard. Thus, I'd like to provide general insights applicable to both places.
During the day, the central and business districts of these cities are generally safe, as long as basic tourist precautions are observed, such as avoiding displaying large sums of money. That's the key to a worry-free experience.
On the outskirts during daylight hours, consider the following: avoid flaunting expensive cameras or gadgets, refrain from showcasing high-end smartphones, keep valuable jewelry hidden, and opt for a small front-carry backpack for added security.
Nighttime ventures into these areas are best avoided, but the choice is ultimately yours. Personally, I've explored nearly every corner of these cities, and all has been well.