Just 2 weeks ago I was in Pattaya together with my wife and son. We flew to Suvarnabhumi Airport in Bangkok and booked a taxi in advance to bring us to our hotel in Pattaya. The taxi service we used is called 'Taxi Airport Bangkok'. It was 1,700.- THB for one way. The trip from Suvarnabhumi Airport to Pattaya is around 1 hour 20 minutes. And of course we also booked the trip from Pattaya back to Suvarnabhumi Airport one week later. Very good taxi service. Here is the link:
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(but if you prefer you also can buy a bus ticket from Suvarnabhumi to Pattaya. The bus ticket counters are in the basement of the airport).