And with traveling I mean going from place A to place B. Of course it depends on how much time you have and your reason for traveling. But remember traveling from one place to another place is part of the journey. There are a few options for traveling in Thailand .... you can travel by bus (but I would recommend never to take the night-bus for long distances), train, air-plane or you can rent a car and drive yourself (but I would recommend not to drive at night or with bad weather like rain).
Traveling by public transport like the bus & train has the great advantage of being part of the local way of life and meeting people. That is why you are traveling, right? The downside is that you are bound to the routes and time of public transport. Although there are going busses from almost every place to almost every place in Thailand. Enjoy the local way of traveling, meet local people and see the real culture of Thailand.
My personal tips ....
In Bangkok travel by public transport like the Express boat, Skytrain (BTS), Subway (MRT) and at least once take a TukTuk (for a short distance).
Traveling from Bangkok to Chiang Mai? Take the night-train to Chiang Mai and travel back by bus and make some stops at example Lampang, Sukhothai or Ayuthaya.
Traveling from Phuket to Chiang Mai? If you have not much time ... fly. Otherwise take the bus to Bangkok and then the train to Chiang Mai. But NOT take the long-distance bus that goes "straight" from Phuket to Chiang Mai!