The Regulation of Airspace and Radio, specifically mentions that you can not fly in a 9km radius around most Airports.
in addition, there are quite large patches of areas that are designated “NO-FLY-ZONES”
the CAAT publishes KML/KMZ files with exact coordinates of No-Fly Zones, you can directly download them here
or download the files from Jul 2021 from 0x8.in.th [Aerodome, No-Fly Zones]
Cropping out the part where flying is widely permitted are
parts of Ayutthaya, Northeast of Saraburi, Northeast of Pathum Thani, North & East Pathum Thani, Rangsit (minus the 9km around the Airport), West & Sout of Nakhon Nayok, Kabin Buri, East & West of Prachinburi, Northwest of Kanchanaburi, almost all of Chachoengsao, MinBuri, Samutprakan (minus the 9km around the Airport), Chonburi, West of Sa Kaeo, West & South of Chanthaburi, Samet, Rayong (minus the 9km around the Airport), Northwest of Trat (minus the 9km around the Airport), West of Ratchaburi, a small area around Surat Thani, South of Nakhon Si Thammarat, South of. Phang Nga, Trang, Songkhla, Krabi, Phuket, South of Narathiwat
Bangkok (special area)
Bangkok generally is a Special area
as of Jul 2021, the zone created for the Royal Cremation Ceremony of His Majesty the Late King Bhumibol Adulyadej in Sep 2017 is still there.
it is unclear to me if the Special regulation about this area is still active at this time, so be careful, and make sure you got permission when flying in BKK.