West Stowe Country Park - St. Edmundsbury Borough Council. Within approximately 10 minutes drive. This can be an excellent place for a family visit with a reconstruction of life in an Angle Saxon Village plus a Visitor Centre, cafe,  and Museum showing historic finds.
Web Page - http://www.stedmundsbury.gov.uk/sebc/play/weststow-asv.cfm

River Lark - Enjoy a walk along the river between Mildenhall and Bury St. Edmunds - A local walk.
Web Page: http://www.ldwa.org.uk/ldp/members/show_path.php?path_name=Lark+Valley+Path