Go to Hyderabad - book room in medipatnam - then get a bus and book full day ticket 80/day..you can travel as much as you can -- if you go by cab then you can't see everything freely bcz places are more and time n charges are more ..so you need time for visit
There are many local travel agencies in Hyderabad. But few well known agencies are
1. Southern travels
2. Telangana State Tourism Development Corporation
These are officially recognised by ISO and u can know more through these links:
Telangana Tourism. For more details of places to visit DM me :)
Hyderabad is a big city, you can know everything about it on google and you can reach anywhere in the city with the city transport, so it's better to roam on your own, you can also hire a cab and driver to roam you around.