First of all, you need to know that there are two different Bangkok airport, so make sure to not mess that up. They are quite far apart so it makes a difference. I have been to both of Bangkok airports.
How to get from Suvarnabhumi to Bangkok city center
I was hoping to hop on the public bus, but I ended up not doing it. I didn’t see any clear instructions on where to head to hop on the bus, so I had to ask some locals who finally told me that it should be in front of column 8. In column 8 I saw no bus sign and no sign of any sort of bus, or either people waiting. Feels like this Bangkok airport doesn’t have good bus connections. I ended up asking someone else who told me that the bus is not so frequent so I easily gave up on that idea because I saw an easy Skytrain connection heading to the city.
First, I took the Skytrain to Makassar which cost me 35bh. In Makassar, I had to change to the MRT line, metro. From Makassar, I bought a ticket to Sam Yot for 37bh. Sam Yot is the closest MRT station to Khao San Road. From here I simply walked to my hostel 15 min away, but you can opt by ordering a Grab, or something else. I landed at 7.30 pm at the airport and at 9.30 pm I was at my hostel. I haven’t bought a SIM card yet. I bought it at 7- ELEVEN as I walked to my hostel for 199bh for 1 month of internet but not unlimited. I was only gonna stay for 7 days, but the 7-day package was more expensive lol. At Suvarnabhumi Bangkok airport, I didn’t check the prices, but I’m sure they were more expensive.
Don Muaeng airport to Bangkok city center
There is a cheap public bus operating from Don Muaeng Bangkok airport, or better, several ones. They have different destinations so you might check first which one is the best for you. I took a picture at the airport that could help you plan this ahead:
Also, there is an APP to track the buses in Bangkok, it is called ViaBus and will show you the buses in real time, and plan routes for you, basically it is a very useful tool if you plan to visit around by local bus while staying in Bangkok. It comes in very handy so you might want to download it: ViaBus
This was the airport where I left Thailand. It was easy for me to access it because I stayed in the Chatuchak area which is not that far from the airport and in less than 40 min I was at Don Muaeng airport. I hopped on the bus very near Chatuchak market. There were several options but I hopped on number 510 which doesn’t stop right at the airport but on the street next to it, which wasn’t a problem because it was only crossing a footbridge and I was already at the airport. Was easy but I had to ask for help on the bus to know exactly at which station should I leave. From the place where I hopped on the bus, I had these options: Bus n 29, 59, 510, and A2, which are the only ones that really stop at the airport entrance. 30 bh should be enough to take you to the airport by bus.