Long-ish answer warning! Here's a summary:
The only guaranteed-to-be-safe method of travelling to and from Corregidor:
Sun Cruises Ferry which has trips to and from Manila and also a ferry to Bataan.
If you're ok with less-safe methods that could be less expensive, try:
Pump boats from Mariveles: (text 09206480486 or 09277904684)
And here's one thing ...
Here is what has worked for me in South Korea. Pretty sure that most of this applies also to Cebu.
You can try to use social networks. There are certainly expat groups on Facebook. Search Expats in Cebu or Foreigners in Cebu. You can also search for more specialized groups such as French in Cebu, Expat Mums in Cebu, Hiking in Cebu...
Virtually any country or city with a foreign community also has an expat forum online, and these often organize social get-togethers. I'm not familiar with the Philippines expat scene, but googling "philippines expats forum" returns a whole slew of results, and there's at least one forum dedicated for just Cebu as well.
There is no one solution for this. Some suggestions...
Hash House Harriers.
@Taladris' answer made me realise there are more:
Here are two more that I often check for:
Facebook events (with an ...