You are absolutely right! All of those cities are great and definitely worth visiting. I would add Cluj-Napoca to your list as well. It’s the second largest student city in Romania, loaded with bars, cafes, clubs, and everything else that students (and backpackers) love to do. It has similarly impressive architecture as well as interesting history, since it was the capital of Transylvania when it used to be an independent region. Plus, the whole city is surrounded by stunning nature. AND, (prepare for shameless plug now) it’s home to Transylvania Hostel, one of the finest hostels in all of Romania!*
*(There is a small possibility that this opinion is slightly biased, since I’m the owner)
Romania is a fantastic country that is highly underrated, and frequently suffers an undeserved stigma among backpackers. It’s beautiful, it’s inexpensive, it has fascinating history, the young people speak wonderful English… There are so many reasons for backpackers to love it!