Now, I haven't lived in India for a full calendar year yet, but borrowing from a variety of sources, the best time to plan a visit to Hyderabad -- and most other parts of India -- is October through February, although you can usually get away with March and September, too. Weather should be a factor in your travel plans. April and May, go the rumors, are too hot to be pleasant. June, July and August are that unpleasant combination of hot and wet. Steamy. Blame the monsoons.
But depending on what you'd like to see/do, there might be more specific suggestions:
Sightseeing in Northern India's "GOLDEN TRIANGLE" (Delhi, Agra and Jaipur)
If you want to hit the Taj Mahal, the ancient and modern palaces of India's capital and Rajistan's beautiful desert capital, plan to avoid the hottest months of the year, unless 50 degrees celsius is your thing. The "winter" months of November through February are most pleasant.
Hiking in the HIMALAYAS
From west to east: Jammu and Kashmir* (Srinigar), Ladakh (Leh), Himachal Pradesh (Dharamsala, Simla), Nepal (Katmandu), Sikkim* (Darjeeling), Bhutan*, Arunachal Pradesh*
* Some restrictions apply.
In Ladakh, weather is extreme. Think Colorado, except next to Kashmir. Most passes don't open in late June. Summer season for hiking is July and August. Autum trekking extends from September to the first half of October before it gets too cold again.
If you're hiking out of Darjeeling or into Sikkim, plan around the monsoon. Spring hiking is possible between March and May. Fall hiking is possible in October through December.
Relaxing along the coast and backwaters of GOA & KERALA
The beaches of Goa are best savored between October and March. April through September just aren't as pleasant.
Keralan houseboats are good any time of year except the June and July monsoons. The peak season is the December through February winter.