If you are going to book a flight to Bangkok, and luckily there are two airports available for you which are Suvarnabhumi Airport and Don Muang Airport, and you want to choose the one that is closer to Bangkok city center, here is the answer.
Bangkok has 2 airports: Suvarnabhumi Airport and Don Muang Airport. Suvarnabhumi Airport is actually located in Samut Prakan Province, around 25 kilometers from Bangkok city center, and currently is the main airport. Don Muang Airport is located on Vibhavadi Rangsit Road in Bangkok, and currently is used by many low cost airlines.
So, to answer the question, Don Muang is geographically closer to the city center.
BUT Suvarnabhumi Airport offers better transportation mode to connect you to the city center. And, I recommend you to consider that!
Suvarnabhumi Airport connects with Airport Rail Link which connects to the BTS Skytrain, while Don Muang Airport does not connect with any express rail. From Don Muang, you need to take a bus around 30 minutes or so (depending on the traffic) to reach the BTS Skytrain.
If you plan to take a taxi from the airport to the city center, from Don Muang might be cheaper. But if you plan to use public transportation, from Suvarnabhumi Airport might be more convenient.
Well, I would say that the transportation cost from both airports to the city center is not much different. If I were you, I would consider the flight fare too.
Hope this information helps
Updated 15 June 2019
Below links are an estimated taxi fare from both Airport to popular places.