Already positioned on the road that leads there
Attapur is a residential and commercial locality in south-western Hyderabad, close to Mehdipatnam and Rajendranagar. That location happens to matter a lot for an Anantagiri Hills trip specifically: one of the common routes to the hills runs via Mehdipatnam, Chilkur, Moinabad and on to Chevella — a corridor Attapur sits right alongside, rather than needing to reach via a longer cross-city drive first.
That makes this a direct starting point for this route, unlike pickups that typically need to join the Outer Ring Road from further north or east before heading southwest. Anantagiri Hills itself, near Vikarabad, is known for coffee plantations, trekking trails ranging from an easy temple walk to longer forest routes, and the Anantha Padmanabha Swamy cave temple; it's also the source of the Musi River that flows through Hyderabad.
Given the shorter run, this pickup point works comfortably for a family outing without the earlier start that other parts of the city would need for the same day trip.