I agree with Ilja that your best option if your heart is set on Brasov is to fly into Bucharest from where it is a 3 hr journey (train) to Brasov.
If however, your constraints are to fly into either Chernivtsi or Odessa, then your options are not very good (assuming you want to get to Brasov by train/bus/mini-bus and not fly into Bucharest. Caveat - I am no expert at this - I've just looked at a lot of the crossings into Ukraine (we are headed there in August) to figure out the ones with the least hassles.
Here is what I think your options are (you need to do further research to confirm this) - try the LP thorntree forum and post there or try tripadvisor's forums.
From Chernivtsi - cross the border to Sucavea in Romania using marshrutky or the one daily (morning) scheduled bus (per LP). From Sucavea take a train or bus towards Bucharest and figure out an appropriate place to switch in order to get to Brasov (try Deutsche Bahn). If you have to go all the way to Bucharest, LP indicates this will take 7 hrs.
From Odessa, your best bet is probably as follows Odessa-Chisinau (Moldova) 6 hrs - Bucharest (13 hrs) - Brasov (3 hrs) or from Chisinau head to Iasi (2 hrs) and from there try to get to Brasov.
Either way, this is not going to be an easy journey.
Do let us know if you find an alternate route.