Theoretically, wi-fi and 4G internet access is available in much of the Philippines. However, the reality is a different story. It's frequently not working, intermittent or very slow, especially in the provinces (Palawan being the poster child for dysfunctional wi-fi).
That huge caveat aside, most hotels, cafes and restaurants in touristy areas and provincical centres provide free wi-fi.
For smartphone users, local SIM cards with data (4G) are easy to purchase, and data is cheap at less than P50 per day.
Not travelling with a computer? You can still find internet cafes in most decent-sized cities. Business hotels and an increasing number of boutique hotels and hostels have computers for guests to use.