Hey, You can visit Kudremukh which is a popular trekking destination in Karnataka. During monsoons the place would be lush green and soothing to the eyes.
If you are into mountains, then Chikmagalur is a good option. It is best experienced with Homestays. Homestays that are tucked away deep in the mountains are a relief from the Bangalore city chaos If you like to visit waterfalls, then Shivanasamudra can be a great place. If you are seeking some cultural experience, you can head over to Janapada Loka, a folk museum on Bangalore - Mysore highway. (Check my post 'Weekend Getaways from Bangalore', for more details)