Kindra!
I'm quite baffled because you want to visit Romania. It's a beautiful country, too bad romanians live her.
Firstly, you should definetly come here in summer. It's quite hot, but I think this shouldn't be a problem. I suggest you to come in summer because in this way you can see somethings, which can't be seen in other seasons.
Romania is famous for it's mountains and woods but let's not forget about Count Dracula and & co. In this way you should visit Bran Castle, Vlad Tepes a.k.a Count Dracula's castle, nice place if you like old buildings and creepy valleys.
Other choice can be Moldova Monasteries. If you want to see what means a life without TV, computer, cell phone, a life based on praying, feeding the animals, praying and so on, if you want to eat mashed poatatoes with pickles or other "diet stuff" this is for you! If you are a troubled youngster this is a place were you can recharge your batteries, spiritual ones, (talking from my experience, been there done all the stuff I had told you about.)
Well there are lots of nice places in our country; you can visit them without much money and I guarantee that you will have a great time.