If you want to come to Tokat by plane, you'll have only one choice: Atlasjet. This local company is the one and only which has a direct flight between Istanbul-Tokat. I am not sure if there are other options for Ankara or Izmir, but I don't think so.
As a person who lives in Anatolian part of Istanbul, I prefer to use Sabiha Gokcen Airport. Unfortunately Atlasjet uses Ataturk Airport.
Prices are differing between 49 ytl - 139 ytl for one way. Tax is not included.
The most convenient to come to Tokat is either by car or by bus. Topcam Tourism is the most widely used bus company. It has buses to Sivas (105 km), Amasya (115 km), Ankara (440 km) and Istanbul (800 km).
Topcam is one of the oldest bus companies in Turkey. It is also the name of a location in Tokat.
The company founded in 1961 and it's first destination was Ankara. Since my grandparents was living there and Tokat was my birthplace, Topcam is the bus company I used the most.
It is 790km between Tokat-Istanbul, and it takes 12 hours. The ticket price is 50 ytl (27 euro or $35). It is possible to buy tickets online but unfortunately they do not have language option. You have to know Turkish, or ask for help.
And here is a story: Do you like movies? In a Turkish movie called Vizontele Tuuba (Vizontele is the deconstructed version of television) one old Mercedes bus used. It is belong to Topcam. And as a "Things To Do" tip, you can see this old and cute bus in Tokat terminal.