I have been to these places from Bangalore and would definitely recommend them! (distance is from Majestic Bus station)
Nandi Hills: 60km
Saavandurga: 57km
Bannerghatta: 36km
Wonderla: 37km Sakandagiri Hills: 60km
Big Banyan Vineyard: 29km
Big Banyan Tree: 28km Shivagange: 48km
Here are a few spots 50km away from Bangalore Savandurga hills is 50km away
Jain farm 7kms away
Grovers vineyard 40kms away
Bannerghatta park 22kms away
Muthyala maduvu 40kms away. Other spots are Kempegowda fort, thottikallu falls, Turahalli forest and thattekere.