Hi, Anne, first, I think that Bucharest deserves 3 nights. There's a lot to see and do there, and while it's not a second Paris or even a second Budapest, it's a very interesting city with a lot of charm and some interesting sites. Since you are not visiting Maramures, I would strongly recommend seeing the “Dimitrie Gusti” National Village Museum, which has over 300 historic rural structures, including authentic peasant houses, wooden churches, barns, and 17th-to-20th-century windmills that were dismantled and relocated from various ethnographic regions of Romania. Some of them are really amazing to see. I spent hours there and loved it.
We each spent around 6 to 8 nights alltogether in Bucharest, although I don't think you need to spend that much. We did spend 4 nights in Brasov, and I loved the city, but I think 3 nights would work well also. We spent two nights in Sibiu, although I really loved that town and I could very easily have spent another night there. But I think 2-3 nights works well there.
1-2 nights in Sighisoara would be fine as well. I don't think you really need 3 nights in Cluj-Napoca, but that's up to you. We weren't there for that long (only 1 night), and I think all three of us would have liked more time there, but you could probably see it pretty well in 2 nights. I really liked Timisoara a lot as well, but you probably don't want me adding additional places to your itinerary, lol!
As far as hotels, our guide chose the Sighisoara hotel, but I liked it very well. It was charming, included breakfast (and also had a restaurant with wonderful food for dinner), and was in a great location. It was called Boutique Hotel von Graf. And it had the best Papanași dessert that I had in Romania. I strongly suggest having that dessert at least once on your trip.
In Bucharest, I stayed at the Scala Boutique Hotel, which I liked very well. It was in a convenient location and included a very nice breakfast. The staff was very pleasant and the rooms quite large and very ornate. At the end of the trip, I stayed at an apartment I found on booking.com that was right off Calea Victoriei near Strada Știrbei Vodă and was a great location. There was so much to see and do in that area.