Bangkok – ถนนวิภาวดีรังสิต
Well if you are in the same situation, I would definitely recommend to take the train called Airport Rail link (ARL) to Phaya Thai (terminal) and then take the sky train (BTS) or tube (MRTA) depending on where you are staying. If you are not too sure where to go, ask the information counter before heading to the train ticket machine as they are very useful. They gave me a transport map and showed me where to go on it.
The train from the airport to city center is very cheap 45 baht which is approx. £1. Same for the tube or sky train, it never gets higher than 90 baht.
Transport from Bangkok BKK airport to city center
The cheapest and quickest way to head to the centre of Bangkok is by train.
It is in the airport easy to find (follow the sign) and will cost you 45 baht to Phaya Thai terminal.
From there you will have to take the sky train or tube depending on where you are staying.