What is the process for completing a 90-day report with a DTV Visa in Bangkok?

You can use agent, or you can also do it at post with registered mail if your address won’t change (they’ll send back the paper to your address). Reportedly costs 70-80 baht with Ems tracking. Keep copy of everything, process and address is on immigration website

There is no "best place to do it" there's ONE place to file a 90 day report in person in Bangkok on a DTV and that's at the main immigration office out at the government complex Building B, Section A inside the immigration office

you need the TM47 form and using the address where you have a TM30 filed (they will sometimes check that you have one on file)

OR

You go to Bumrungrad Hospital on the 10th floor in the Business Center, and they'll do a 90 day report for you for 650 baht. You leave your passport with them, they send the runner with a PILE of passports, do the 90 day report then you can pick your passport back up