I spent 17 days in Romania last summer, but I'm afraid I don't have much specific information for you. People still wear traditional costumes on Sundays up in Maramures, the northwestern part of Romania known for its beautiful wooden churches. At a couple of the more visited churches, there were folks selling embroidery and other items. I'm no expert, but I had the feeling that the embroidery--or at least some of it--really was produced locally. I realize that's not the type of sales venue you're asking about, but I'd guess that Maramures might be a place to look for embroidery.
Romania has a lot of forests, so woodwork is popular. A lot of the homes in Maramures have huge, intricately carved wooden gates; those aren't for sale, obviously.
Pottery production also seems big. I happened to hit Sibiu's outdoor ceramic market (early September last year). The city has a pretty historic district but doesn't seem heavily visited by western Europeans. Most of the shoppers seemed to be Romanian; they were buying functional pottery for everyday use. There were some vendors with different styles of work, but much of it followed what I assume are traditional patterns. Costs were generally low.
Aside from seeing what pops up in Google, I'd suggest stopping at the tourist office as soon as you reach Bucharest and Brasov. I found the T.O. personnel very helpful.
For future reference, my favorite shopping experiences in many trips to Europe were in Bulgaria. Again, lots of pottery, but of a more contemporary style. Also inexpensive jewelry.