First, Romania is easily worth 5, 6 or 7 days. If you are doing that and ending in Bucharest then you have a lot of options. First you have to decide if you will enjoy long, long leisurely train trips or can afford a private transfer or if your time is precious and you are willing to fly. To the best of my knowledge there is no route out of Bucharest to a major European destination that is shorter than 10 hours. Even the drives to major cities in adjacent countries are pretty long.
Flights open up more possibilities. Budapest and Prague are both under 1.5 hours and under $100 as is Sofia. I’m not a big Prague fan, especially if you want to see something “real”. For Real I would think of getting a guide to pick you up in Bucharest and drive you to Varna Bulgaria and then spend a week seeing Bulgaria. A stunning country with few tourists and lots of amazing things to see. Guide and Car would run you about $200 to $250 a day, the hotel another $50 for some pretty nice places. You can fly home from Sofia.
Or if you want a little more familiar comfort with architecture described by Anthony Bourdain as: "If there was such a thing as building porn, it would be this", then go to Budapest.