White Mughals by William Dalrymple is the essential read: the definitive account of Hyderabad under the Nizams and the extraordinary entanglement of British officers with Hyderabadi court culture, centred on the love affair between James Achilles Kirkpatrick and Khair un-Nissa. Rich on the city's streets, architecture, and politics.
City of Pearls — any good account of Golconda's diamond trade and the Qutb Shahi period fills in the history the monuments don't fully tell.
Lonely Planet South India & Kerala or the equivalent Rough Guide to South India both cover Hyderabad well as part of a broader South India trip.
In Other Rooms, Other Wonders by Daniyal Mueenuddin — Pakistani short stories with strong Deccan cultural resonances, useful context for the feudal and courtly world that shaped Hyderabad.