You have many things to see in Transylvania, depends what exactly do you want to see. For medieval towns don't miss Sighisoara, Sibiu and Brasov. If you like nature you can go to Fagaras Mountains, the highest from Romania or to Apuseni Mountains, with many caves, quays and so well preserved countrystile life. Also, if it's interesting for you, here you can find many saxon churches, from which seven of them are counted on UNESCO World Heritage List. I advise you not to miss Biertan (near Sighisoara), Carta (close to Fagaras) Slimnic, Valea Viilor and others (Sibiu - Medias - Sighisoara road). We have also castles and fortress, the most interesting are Hunyad Castle in Hunedoara, Bran Castle and Rasnov Fortress, both near Brasov.
In my opinion, the romanian Black Sea coasts don't deserve the effort to be visited, there are not many things to see there, but if you want to go a better choice would be, as Ktack also says, to go in Danube Delta and spent there few days.
Good luck and have a nice stay.