Can I apply for the DTV online from places outside Manila, like Cebu or Palawan?

the ThaiEVisa.go.th website is the only method to apply for and submit any Thai E–Visa application to any Thai Embassy/Consulate around the world....

You need/should be physically in the respective country throughout the Thai E–Visa processing process, and, if necessary, be available to attend an in-person interview at the Thai Embassy/Consulate where you submitted your Thai E–Visa application....

Now, if one were to make visits to Puerto Princessa, Cebu, Davao, Laoag or elsewhere, then that's fine, as long as you as a Thai E–Visa applicant are fully cognizant that the potential of making a visit to the Thai Embassy may or may not be necessary....

You apply online via that site and can apply whilst in another part of The Philippines. If asked for an interview you would need to go to Manilla.