I lived in Bucharest, Romania for 4 years. The country itself is very beautiful. I would suggest a tour guide. I believe if you search the internet you will find an official tour Romania web site. Some things to do: Brasov - a great mountain city with an enchanting town square, Peles Castle - I must have been there at least 20 times but saw something new evertime, Bran Castle (AKA Dracula's Castle), Sigisoara - a fairly well intact medievial town, Constanta - a Black Sea beach "resort".
Bucharest is a must, but I would be real careful. There are lot's of pickpockets and thieves. In Bucharest, definetely see the People's Palace and take the tour. Drive by the Arch de Triumph. Have dinner at a traditional Romanian restaurant just watch out for the local drink known as Tuica or Palinka. It's a very potent plum liqour.
Prices were cheap when I was there, but I understand the exchange rate from dollar to Lei is worsening.
If you take a taxi, agree on a price before departing. Most don't use meters even though it's the law.
Hopes this helps.