The Romanian dish I can recommend is the soup, "Ciorbă" (pronounced like 'chorba'. It's described in the Wikipedia as...
Ciorbă (Romanian pronunciation: [ˈt͡ʃorbə]), from Persian shorba
(شوربا), via the Turkish word çorba, is a general Romanian word
describing sour soups consisting of various vegetables and meat. Most
Romanians differentiate between "supă" (soup) and "ciorbă" by the fact
that supă has no added acid and is usually clear
Generalization: Regional variants on this soup are ubiquitous across eastern Europe. I use the Russian word, "солянка" (pronounced 'solYANka' in speech) regardless of where I am and admit that the word may be subject to regional interpretations, but is always immediately understood and always delivers up the same basic recipe. My own favourite variant includes black olives. In addition to being a great food, it's a powerful remedy for hangovers. However, if you require localised precision, it's best to stick to the Romanian word, Ciorbă.
Some of variants to this dish which are claimed by Romania as a national dish are listed in a scan I made of Lonely Planet Romania & Moldova...
Source: Scan from 'Lonely Planet Romania & Moldova, 1998, Lonely Planet Publications, Nicola Williams (Author), David St. Vincent (Author), fair use
The other food I recommend is Frigărui, described in the Wikipedia as...
Frigărui1 (Romanian pronunciation: [friɡəˈruj], singular: frigăruie)
is a Romanian dish consisting of small pieces of meat (usually pork,
beef, mutton, lamb or chicken) grilled on a skewer, similar to the
kebab. Often, the pieces of meat alternate with bacon, sausages, or
vegetables, such as onions, tomatoes, bell peppers and mushrooms. It
is seasoned with spices such as pepper, garlic, savory, rosemary,
marjoram and laurel.
Again, this dish is ubiquitous across eastern Europe and nearly every country stakes a claim on it as a national dish. For example, it has the singular distinction of being pictured on a postage stamp in Tajikistan. Families head for the forest on weekends, prepare a fire, and cook it out in the open. The English equivalent is 'kebab', and Russian is "шашлы́к" (pronounced 'shashlik'). Both English and Russian work equally well for this food in Romania.
Turning once again to the Lonely Planet, there's a restaurant recommendation...
If you have the opportunity to mix with locals and weather permits, I recommend joining a family for an excursion to the forest for 'kebab'. Along the way you will have a wonderful chance to learn about mushrooms because these are collected along the way (by experienced family members who know what they are doing) and used as ingredients.
Obiter dictum: If you are flying in to Bucharest, insist on finding your own taxi to your hotel.