I've been to several of those places, so I'll get you started. InYourPocket.com has downloadable guides to some of your destinations; they are a good source of sightseeing information.
Pécs is quite an attractive town, home to the Zsolnay ceramics company. Zsolnay was the first company to create glazed ceramics for outdoor use. The best collection is at the museum in the Zsolnay Quarter. If you're really interested in decorative art you'll also want to go to the other ceramic museum in the city. You'll also see a lot of the ceramics used on the exteriors of local buildings (and scattered elsewhere in Hungary). The Zsolnay Quarter isn't right in the center, so take a taxi if there isn't a convenient local bus.
Novi Sad has a quirky old town with a sort of hippie vibe. It's fun to wander around. I'm not sure how far the historic area is from where your cruise docks. It's quite some distance from the train station, but there are local buses. I am not sure about indoor sightseeing in Novi Sad, but there must surely be some.
Belgrade has a more "foreign" feeling than most of the other major cities in the Balkans. There is some very pretty architecture in the historic center. I basically just spent a day wandering around while I was in transit, but there are definitely historic sights and museums. English wasn't particularly widely spoken in 5 years ago, which contributes to the feeling that you're somewhere different.
A few comments on Serbian food: Serbian menus often list optional sauces/condiments that cost very little; I think I paid about $1. I highly recommend trying them; they really dress up something like a chicken kebab. I liked ajvar, which is based on sweet red peppers. There's also a tasty mild cheese spread--I think called "kajmak"; one restaurant mixed the two together, and it made a great appetizer spread on the local bread.
In Serbia you'll often see stands (and probably also bakeries) selling cheese pies/pastries, typically prepared in large sheet pans and cut into rectangles. They're made with flaky pastry (like phyllo) and somewhat similar to Greek tiropita. Googling indicates the Serbian version is called "gibanica". I remember having it in unsweetened form, but I wouldn't be surprised if there's also a sweet version. This is a yummy, if calorie-laden, breakfast or snack, but it can be messy since both the cheese and the pastry are oily. I always carry a ZIP Lock bag with me for purchases like this.
Bucharest is not an especially attractive city; Ceausescu amused himself by knocking down most of the historic buildings and replacing them with ugly modern stuff. But there must be some interesting museums. This would be a good place to go to a historical museum that covers the events of the Ceausescu era. Trying to see very many of the remaining old buildings would probably entail a lot of walking.
Rousse is "Ruse" in Bulgarian. I've read that it has a nice historic center.
Brasov has a rather large historic area, great for wandering. It's one of Romania's prettiest cities. One thing I appreciated about many of the tourist destinations in Romania (and I believe this applies to Brasov, but my memory isn't 100% clear) is the prevalence of plaques on old buildings that tell you in what century they were constructed.
Romanian is a romance language, so if you know some French, Spanish or Italian, you'll probably be able to read some of the signs, but the word endings make things look funky.
Romania is a notably poor country by European standard; I'd recommend eating in restaurants targeting tourists--not my usual approach. You'll see large ring-shaped breads for sale, often from bakery windows. They are excellent breakfasts or snacks and come plain (sort of like bagels) or with fillings (some sweet).