Clare boasts a lovely country park with riverside walks along the banks of the Stour, a railway station now defunct and the ruins of a castle, from the top of the castle mound a good view of Clare and the church can be seen
The Priory at Clare you can get permission to walk around this very private place, I found it very peaceful a few years ago
The old Priests House is one of Suffolks gems, they really do not come much better than this, only a 'stones throw' from the delightful church too
http://en.wikipedia.org/wiki/Clare,_Suffolk