A little more than twenty cities in Thailand have an airport and are reachable by plane. Traveling by plane in Thailand is a good solution to avoid long bus or train trips. And it is not always that more expensive. Most of the airlines websites offer good prices. There are several low cost carriers operating domestic flights in Thailand just be carefully about lugage allowance included in the price. You often have to also book an extra bagage fee.
Have a sweater to cover yourself when boarding a plane in Thailand. Sometimes the air conditioning is very cold
Note that there are special bus shuttles connecting Suvarnabhumi Airport to Don Muang Airport. Bangkok Suvarnabhumi has a Airport Link, a skytrain line that takes you from Suvarnabhumi International Airport to downtown and vice versa. Many cities also offer shuttle buses that connect the airport to the city center that are much cheaper than a taxi (unless you are 3 or more people). Ask at the airport information desk.
Cities with airport: Bangkok, Buriram, Chiang Mai, Chiang Rai, Hat Yaï, Hua Hin, Khon Kaen, Koh Samui, Krabi, Lampang, Loei, Mae Hong Son, Mae Sot, Nakhon Phanom, Nakhon Si Thammarat, Nan, Narathiwat, Pai, Roi Et, Ranong, Pattaya, Phitsanulok, Phuket, Sakon Nakhon, Sukhothai, Suratthani, Trang, Trat, Ubon Ratchathani, Udon Thani