The Swan is a great place to eat if you visit Lavenham. It is a 15th century Inn and has a great atmosphere. The food is really nice too.
It also has American ties. In the Old Bar, there are signatures and memorabilia from the 487th Bomb Group 8th AAF American servicemen which were stationed in Lavenham during WWII.
I always eat here when I visit Lavenham and the food is superb. It is in a very relaxing atmosphere. If you do bring your children here, I do suggest making sure that they are on their best behavior as it is a bit up market but I would suggest this in most restuarants anyways.
If you are out there, its worth taking a break and enjoying yourself.