The most practical base for visiting Vemulawada is Karimnagar, 36km away, which has good hotel options and regular onward transport. Hyderabad, 150km to the southwest, is the main hub for international and domestic visitors and makes a comfortable (if long-day) base.
Karimnagar (36km) is the district capital of what was Karimnagar district before the creation of Rajanna Sircilla district. The town has a 16th-century fort, several temples, and the broad Manair river. It is a useful stopping point if you are travelling between Hyderabad and Vemulawada.
Hyderabad (150km, 3h by express bus) is the natural gateway to this part of Telangana — a major city with the Charminar, the Golconda Fort, and one of India's great bazaars at Laad Bazaar. Most visitors to Vemulawada route through Hyderabad.