You can visit Chickmagalur - Kemmangundi. This place is serene with lush greens and lovely hidden waterfalls. This involves trek down the hills and long walks!
P.S: You can completely avoid common public and tourists! The other best option is to visit Wayanad district which is just ~250km from Bangalore. It requires a good 3 days to complete touring the whole district spotted with high rise mountains, natural water bodies, wildlife sanctuaries, scenic Islands, places of historical importance etc.., all coupled with very comfortable climate. Good Luck!!!