There is no Grand Cru - Premier Cru style official classification for the vineyards in Tokaj. However, there are historical unofficial classifications of the vineyards from the 18th and 19th centuries. The classification is mainly important for dry wines as most aszü is not single vineyard (the importance of aszú might be the biggest reason why the classification remained unofficial).
There are of course lieu dit that are better regarded, like for example Úrágya, Betsek or Szent Tamás. This is a very short and somewhat random list… but as a rule of thumb single vineyard single varietal wines of the best producers is what you should be looking for when buying dry Tokaji.
There are strict rules regarding the following styles of wine: tokaji aszú, tokaji esszencia, tokaji fodítás and also what you can label as minőségi (quality). In addition, there are only six grapes that you can make wine of in Tokaj without limitation (there is a long list that can be planted for research with the appropriate license), these are Furmint that all know of and the others noone ever (exaggerating) heard of: Hárslevelű, Kabar, Sárga muskotály, Zéta and Kövérszőlő.