I've never been to Lithuania but visited Bucharest and Sofia briefly in 2015. "Briefly" because my research indicated that neither of those cities was among the most interesting in its respective country. They're both worth a short visit, but I just don't know what to tell you about selecting between them. Sofia does have at least a couple of striking old churches, and Bucharest has some interesting early 20th century buildings, but the latter are somewhat scattered because Ceausescu entertained himself by knocking down historic buildings. There are other attractions as well, including museums.
More physically attractive that the capitals are three other cities that might be viable if you have 3 or 4 days. Unfortunately, public transportation tends to be slow in the Balkans. Figure you'll cover maybe 30 mph. I found the buses and (more limited) trains to be reliable schedule-wise, however.
From Sofia: Plovdiv (about 2 hours by bus) or Veliko Trnovo (at least 3 hours by bus). I found both of those cities, which have stunning historic districts, to be great for craft shopping.
From Bucharest: Brasov (about 2:40 by train or bus). Very handsome historic area. I was very sorry to have just visited Brasov on a day-trip. The many other parts of Romania that I saw and loved are too far from Bucharest for a quick trip.
The Romanian bus system is a bit odd. You don't usually need to pay for your ticket in advance, but you often need to make a reservation ahead of time. By telephone, not by stopping by the bus station. Although the young people you'll meet often speak good English, I was not willing to assume that of the person I would be telephoning at a bus company. Fortunately, Two good Samaritans made phone calls for me.
Another possibility if you do have at least three days would be to try to arrange a private tour with a car and driver. I'd expect the cost of that to be enormous in western Europe, but--especially if there are 3 or 4 of you--it might be relatively reasonable in the Balkans. But I have no idea what the driving conditions would be like in the winter.
This area is fantastically interesting, but it's not terribly suitable for a weekend visit.
If Varna, Bulgaria is a possible flight destination for you, consider flying there in order to see Sozopol and Nesebar. They are historic coastal towns, very touristy during beach season (and quite possibly dead in the winter), but the tiny medieval churches are something to see. Very worthwhile.