November to February is the best time to visit. Days are warm but dry, evenings cool enough for a jacket, and the light is flattering for photographs of Charminar and Golconda. This is also when most of Hyderabad's festivals fall — Dussehra, Diwali, and the kite-flying of Sankranti in January.
March to June is brutally hot, with afternoon temperatures often above 40°C. Avoid unless you can structure your day around early-morning and late-evening sightseeing.
July to October brings the monsoon. It is cooler but the Musi often floods low-lying parts of the old city and traffic grinds to a halt. The compensation is Ramzan (dates shift by the lunar calendar) when the area around Charminar turns into a night food market for haleem, biryani, and sweets.