Cluj has great bus connections with Budapest. Thus, an alternative is to fly to Budapest Ferihegy Airport with a low-cost company, and then shuttle to Cluj-Napoca. The shuttle takes six to eight hours to make the travel. You can find more details here. The train from Budapest is also an option.
For Serbians an option is to cross the border by train to Timisoara and then take a bus, train or plane to Cluj.
If you come from Eastern Europe we would recommend you to take your ticket through Munich (Germany).
Also, take into account that there are direct busses from Chisinau ( Kishinev), Moldova, to Cluj.
From Ukraine, Kiev or Lviv to Cluj-Napoca through Munich (by plane), is around 290 EUR two ways
We will gladly help you find the best (fastes, cheapest) route to Cluj-Napoca, from wherever you are, so please write to us on info(at)t3ee(dot)org