From Hyderabad you have no of options Warangal ( Kakatiya dynasty Temple tour) Ramappa Temple Bhadrachalam Vijaywada Amravathi ( buddhist site) Srisailim Nagarjunkonda Vizag
As you are planning for long weekend so I would suggest you some of these places:
If interested for historical places then must travel to any of these places:
HAMPI
PATTADAKAL
BADAMI
BELUM CAVES From these pattadakal and badami is very close to each other so you can cover famous spots of both the places within the duration. Nextly if you are mostly interested for some adventurous and enjoy the monsoon then must travel to few of these places of Maharashtra : LONAVALA
MAHABALESHWAR
PANCHGANI
BHIMASHANKAR
MALSHEJ GHAT
BHANDARDARA