In terms of diversity of international flights options and time to the the airport , I think TM is the best, it has airport and is at less than 3h to Belgrade airport.
Budapest is at maybe 6h, like Cluj, same distance the difference is that the customs that are closer to Tm have heavy traffic.
If international flights are very important and many, not talking about only Italy, Spain, Uk and De which are a almost a standard in Ro, then all those car travels will get you sick of them and then the logical move is to Bucharest or close by, probably in the North part of B, that way you'll have an easy and fast way to the airport.
I think Airbnb for one month inaa city will give a clue about it.
Keep in mind that we are in June 2 so you need to move to some place in Romania in the following weeks if you want that cheap tax. ,