Istanbul - without a doubt the best. Fantastic food (and I don’t even eat meat, so no kebabs, etc., for me) and so, so much to see. Spent a week there and could easily have stayed longer.
Lisbon - a close second. Again, enough to keep you entertained and interested for a lot longer than a couple of days. In fact, I spent a month there as a student and enjoyed every day.
I’ve loved a lot of smaller cities too, but you’d be looking at day trips if staying longer than a weekend. Split, Turin and Riga top the list here.
Sarajevo is wonderful as other posters have said, but we went for five days in the winter and it was far too long. Many things closed either due to the season or lack of funding. I feel like we walked certain routes once or twice each day! It is very special, though, and the old town is magical to stay in. You could combine with another Balkan city (we flew via Zagreb) or go at a better time of year and do day trips. I’d like to see it in spring.
Are any cities posted so far tempting you, op?