Here are a few places to visit near BR hills
Bandipur that is 2 hours away
Bheemeshwari is 2 hours away
Chikballapur is 4 hours away
Devarayanadurga is 4 hours away
Anthargange is 5 hours away.
On the way from Bangalore you could stop by Shivasamudram falls, biligiriranga temple and gorukana.