Sighisoara

In any case plan on doing trips to locations around Brasov, there are plenty of things to see within 1-2 hours of travel (Sighisoara, old German walled churches like Prejmer or Harman, the Zarnesti bear rescue center, Rupea and Feldioara fortresses, the Bucegi and Piatra Craiului mountains etc.)

5-6 days in Brasov with day trips to Peles castle in Sinaia, Sighisoara citadel, old Saxon walled churches (the nearest are in Prejmer and Harman), Bran castle, scenic mountain villages around Bran (Pestera, Magura), Rupea fortress, the Bucegi or Piatra Craiului mountains etc.

Brasov is great, but also explore Sibiu, Sighisoara, plenty of small to medium sized towns you can visit or base out of.

Sighishora is small but also a good base for visiting some churches around.

In Romania, definitely visit Brasov, Sighisoara, and Sibiu. I spent a summer in a town near Sighisoara and that whole region is great.

Other things to consider are the fortified churches of Viscri, Prejmer, etc, if you end up going to Viscri, a day trip to Sighisoara and it's medieval historical center or Libearty Bear Sanctuary (book in advance for the latter, they have limited spots).

Sighisoara is basically Romania’s Bruges or Rothenburg. Small well maintained medieval town turned tourist spot.

Consider spending a night in Sighisoara instead of returning to Brasov to sleep. It's neat being in the town in the evening, as it really quiets down, and sometimes it feels like you've got the historic centre to yourself.