Hi Shikha, You can try these places near Varanasi
Singhpur Sarnath- 11 km from Varanasi Chandauli - 35 km from Varanasi
Kaimur - 96 km from Varanasi Mirzapur - 60 km Allahabad - 120 km
If u wish to go slight farther, Chitrakoot-khajuraho along with Panna tiger reserve and Maihar can be good option giving you a varied travel experience.