Our trip was over 15 years ago, and we were mostly using the Lonely Planet guidebook for inspiration, but Veliko Tarnovo was more enjoyable than Sofia. Maybe spend your extra day with a night there. Be sure to visit the Tsarevets Fortress on the eastern edge of town.
I wonder how you’re getting from Bucharest to Veliko Tarnovo - train? We rented a car in Sofia, and drove around Bulgaria, before returning it and taking a night train to Bucharest for our flight west. Among the places we visited were Ledenik just west of V. Tarnovo, and driving over Shipka Pass to visit Kazanlak and the 2,400 year old Thracian tombs, the Valley of Roses (rose oil and rose perfumed cosmetics and lotion, plus a wine region), and Stara Zagora. Maybe one of those could be a one-night stay on your extra day.
We didn’t have time to visit the coastal cities on the Black Sea.