A list of some attractions in the 20 to 60 minute range by car from Greetham and their website links:
Woolsthorpe Manor - Sir Isaac Newton birthplace National Trust
Hamerton Zoo Focusing on conserving rare breeds
John Clare Cottage. The peasant poet.
Ferry Meadows Lakes, Parkland, Railway etc
Wistow Corn Maze near Leicester (Only open in the summer). Fun for the kids
National Space Centre Leicester