Ickworth House outside of Bury St Edmunds is a great place to take the kids, the dog or just yourself for a walk. It costs to park there unless you are a National Trust member. If you are going to be visiting a lot of NT places, it is worth looking into joining as it could say you money.
The Ickworth House was started in 1795 but finished in 1829. The Italian inspired Rotunda is very picturesque and a must see.
The Ickworth House has fabulous 1800 acres of conservation woodlands which have livestock (mainly sheep) grazing. In the spring, you will be able to see lambs following their mother around.
It also has a vineyard where the award winning wines started.
There are nine walks to choose from so that you can see all of the grounds and also choose what suits you and your family. there is even the Trim Trail with exercise stations.
I like to take the dog and walk around the estate.
All the Best!
American to Britain