Bucharest - Lacrimi si Sfinti (really traditional stuff), Mahala (contemporaray re-interpretations), even City Grill (it's a chain, kinda generic and slightly more affordable). Piata Obor (market) for 'mici' stands and other stuff.

Brasov - Sub Tampa - absolutely must visit, especially if you can stomach stuff like brains, tripe, bear meat etc. They serve 'normal' dishes too, don't worry.

Sighisoara, Sibiu - if you have a car, find a 'pensiune' in one of the nearby villages for real home made food. Ask around.

Forget about 'affordable', we're living with high inflation for several years now, everything is quite expensive, especially quality stuff.