Chernivtsi has its own small airport serving flights to Kiev, Athens, Istanbul and Naples among others.Other nearby airports are Ivano-Frankivsk, Ternopil, Lviv and Suceava Romania.
Carpatair flies directly to Chernivtsi for budget prices from Timisoara, where you can connect with destinations around Southern Europe.
You can get to Chernivtsi by train either from Romania or from within Ukraine. The train from Kiev or Lviv is probably the best option as they are comfortable and cheap.
There are frequent minibuses from Lviv to Chernivtsi costing UAH 106 as of end-2011. One daily bus serves Chernivtsi from Suceava. The bus from Chernivtsi to Suceava UAH 68 as of end-2011 leaves at 07:00 every day arriving in Suceava in Romania around 10:30-11:00 depending on the number of people on the bus and therefore the time spent crossing the border. The central bus station is NOT close to the train station, but cabs are very cheap in Chernivtsi.