Nagarjuna Sagar is around 180 KM away from Hyderabad and can be easily covered within a day. We started at around 8:00 AM in the morning.. reached Nagarjuna Sagar by 12:00 noon. Had lunch at Sagar town. There are three things that are worth seeing at Nagarjuna sagar. They are (1) The island museum and (2) Nagarjuna Sagar Dam and (3) Ethipothula waterfalls. Unfortunately, when I visited, the gates of Nagarjuna Sagar Dam were closed.
In order to go to the island museum, you need to take the ferry. The island has huge museum and scattered statues belonging to Buddhist Monastery that existed two thousand years ago.
Ehtipothula water falls are around 10 KM away from Nagarjuna Sagar. Make sure that you ask for directions from the locals.