Most international folks fly into Laguindingan Airport, about 45 mins west of the city. Fixed rate vans and taxis are right outside arrivals, easy to sort, and the drive into CDO takes roughly 45 mins to an hour depending on traffic. Budget extra time if you have a connecting trip or booking to make - philippine city traffic doesnt care about your schedule!
From Manila its 1.5 hours by air with Cebu Pacific or PAL, multiple flights daily. From Cebu an overnight ferry is also an option and some travelers prefer it - you arrive in CDO in the morning and skip a nights accomodation cost. Both work fine, just depends on what youre optimizing for.
Getting around CDO itself is tricycles and jeepneys mostly - cheap and they go everywhere but the logic takes a day to figure out. Grab works in CDO and is honestly the easiest option for airport runs or longer city trips where you dont want to negotiate fares. Download it before you land, seriously.
For Camiguin you take a van from the CDO terminal to Balingoan port, about 1.5 hours, then ferry across to the island. Hotel staff know the current van schedule and can point you to the right terminal, ask them the evening before you plan to go. For rafting the operators can arrange hotel pickup directly which is very convenient.
Parking at the hotel exists but its limited and the city center is dense so space is always a bit of a competition. If youre renting a car for day trips just be mentally prepared for CDO city driving - it has its own rules and logic that takes about a day to absorb, after that its fine!