In Romania :
Bucharest - Villa Helga. It is a hostel close to the center. Super friendly and clean. Good price. Loved it.
Sighisoara - The prettiest city of Transylvania. Hometown of Dracula (but not where the castle is, that's Brasov). I lived in a private home, in the old town. Gorgeous, beautiful, awesome ! What could I say more to convice you ? Great family that pampers you. Since it is a private place, please send me a private message or email if you are interested in getting their address.
The Maramures - North West of the country. Where you'll find the old romanian culture preserved. Lots of people, including children and teens, are still wearing traditional outfits. To arrange lodging in private homes (hotels may be out of price for some of our backpackers, and it is anyway a better experience) and activities in the area :
www.vaduizei.ovr.ro Unforgettable moments.
In Hungary :
Budapest - The Back Pack Guest House. A bit far from downtown, but lovely garden (with a clothes line) and friendly laid-back staff. Big and small dorms with groovy names, and "The Love Shack" the one private room. When I was there, they were celebrating their some number anniversary, we had free food and beers and we all went out to party. Some ex-guests even came from abroad to celebrate with them.
Eger - Worth seeing ! The Tourist Motel is the cheapest place but very decent also.