There were two lines that went off of Hamilton-Wenham. The first and most famous was the Essex Branch that went across the current parking lot of the shopping plaza and headed off towards Essex. In fact there is a book written by Dana Story called "Daily Except Sundays". This book is of the diaries written by Dana's Grandfather, Phillip Adams, who was an engineer on the Essex Branch. If you can get a hold of a copy, it really tells you what a small town branch line was like in the late 1800's and early 1900's. In fact the Walker Transportation Collection has copies of the book. Their web site is here:
http://www.walkertrans.org.
The second is the Asbury Grove Branch that went across Route 1A from the current MBTA station and ended across the street from the entrance to Asbury Grove Camp. This branch line is very hard to trace as there are a lot of houses near or on the ROW, but if you know what you are looking for, traces of it can still be found. There was a station at the end of this Branch that sat up on the hill directly across the street from the Camp's entrance. There were wide wooden steps that went down to street level. A house was built on the depot site 5 to 7 years ago. The Walker Transportation Collection has both a map of the Asbury Grove Branch and a very rare photo of the depot. It is avaliable to view. In fact this was the only depot on the line and the branch was built just to provide a direct rail route for campers to get to Asbury Grove.
There is a third spur off of the Eastern Route in Wenham and that is by the current golf course. It was an ice house spur to Wenham Lake. If you go down/up Route 1A, right along the edge of the golf course by the woods, you can see a flat spot that looks like a ROW. Well, that is it. You can trace it all the way to the mainline. That tiny little spur was worked on by Granville Dodge, who went on to engineer the Trans-Continental Railroad. Hey, you have to start somewhere.
Hope this helps.