Hyderabad and nearby areas have excellent mangoes: Banganapalli/Safeda, Himayat, Benishan; juice mangoes "pedda rasaal" (literally, "large and juicy" - think family size) and "chinna rasaal" ("small and juicy").
Even better, mangoes are at peak quality in May; once the monsoon rains arrive in early June, the quality goes down. Neelam is good through June.
There is also ICRISAT (International Crops Research Institute for Semi-Arid Tropics)
Tourism options in and around the city: Charminar, Salar Jung museum, Golconda Fort, the bazaars in the old city area.
Wherever you go it is mango season in India, so enjoy your trip.