Hyderabad is bang in the middle of Telangana, it should go to Telangana. The people of Hyderabad are either from Telangana or migrated here from elsewhere. My family, for example, came here 400 years ago from the north.
Hyderabadi culture is certainly unique, but a lot of that culture is evident in most districts of Telangana - the people speak a kind of local Urdu, which I speak too. Exposure has meant that many non-Telangana inhabitants of the region have also started speaking a bit of this Urdu. And then there is the kind of Telugu we speak, or the Telugu songs we learned as children - a mix of Telugu and Urdu - so there is much Telangana influence too.
Of course, all cities, countries, and states are dynamic; they keep changing and growing. Still, I would prefer to see Hyderabad rediscover its original personality. There was hardly any history of communal violence in the city (except in the days just before Independence) because there were conscious attempts by the Nizams to create a composite culture, and even earlier under the Golconda dynasty.
The plural character of the place dates back to its founder Quli Qutb Shah, who ruled from the fort-city of Golconda. When Golconda got too crowded, it was hit so badly by a plague that the king had no choice but to move to the plains. So he came down from the hill and built Hyderabad city. It was here that he married Bhagmati, a local woman who was basically a courtesan. As a prince, he would cross the river even when it was in full spate to meet her. His father didn't protest that he was meeting a Hindu courtesan. Instead, he built a bridge to help him cross the river safely!