I have done most of these in my 50 odd years in the county, over the weeks/months I will put up some pictures of the more memorable places
Some memorable ones that come readily to mind are:
Clare Castle Country Park
Knettishall Heath Country Park
Brandon Country Park
Orwell/Bridge Wood Country Park, Nacton/Ipswich
Newmarket Downs
West Stow Country Park circular cycle rides here http://www.discoversuffolk.org.uk/long-distance-cycle-routes.aspx
A 30 minute walk along the River Lark from Mildenhall
http://www.discoversuffolk.org.uk/explore-suffolk-map.aspx?hid=44b6b218-c79d-11dd-99d0-c07756d89593#
Long Melford walk along the disused railway line
http://www.discoversuffolk.org.uk/explore-suffolk-map.aspx?hid=069d1e54-c79d-11dd-bfd7-db7556d89593#
Lavenham to Lineage Wood
http://www.discoversuffolk.org.uk/explore-suffolk-map.aspx?hid=0ac8652e-c79d-11dd-a575-f47556d89593#