The following website gives details of open gardens in villages, where you get to look round several different gardens. A lovely day out with a huge variety usually.
http://www.opengardens.co.uk/open_gardens_in_suffolk.php
Otherwise pick up the National Garden Scheme booklet from Tourist Info office or local library which gives open gardens for the NGS scheme, where people open their gardens to the public for charity.
Other open gardens here:
https://www.greatbritishgardens.co.uk/england/category/gardens-to-visit-in-suffolk.html
Or pop in the library for leaflets.

Oooh lovely thanks

And you're only about half an hour from the truly wonderful Beth Chatto gardens (near Colchester). One of the best in the country!

Ive looked up the Beth Chatto gardens and that's the one for me, it looks phenomenal ! Can't wait. Great recommendation thank you Sheilabub

You're very welcome:)