Boris, if you come to Romania, I wouldn't recomend Bucharest. If you like going in the mountins, you can go to Scărișoara - Padiș (~ 250 km from Nădlac - the border). You will have to camp there, or you can find some houses in the area that wil host you for a small fee - it's really much better than most (cheap) hotels.
If you want to visit cities I would recommend that you spend the night in Sibiu or Sighișoara, or even in Timișoara which is near the border (and then take at least one day to visit some cities from Transilvania - I just mentioned three of them which are worth visiting IMO, you may add Târgu Mureș & several others to the list)...
Heck, if you go to the mountains (Apuseni) I guess I could even let you stay in a chalet that i have there (need to get approval from by wife first, otherwise i might
) - but it will be problematic since in the mountains the locals don't speak english and it won't be easy for you to get any directions there.