With its whitewashed homes and scenic views over the surrounding countryside and coastline, the historic center is most definitely the main "attraction" in Ostuni.
Now, I have to say that if you're not visiting off-season, some areas can feel too touristy not only because of the amount of people but also because there are too many souvenir shops that kind of "cover" the beauty of the whitewashed alleys, but maybe that's just my experience. I wouldn't skip out on Ostuni because of that, and this hilltop city has its charming side too, but I think it's important to point it out.