Bear in mind that New England is much more seasonal than the UK and many things will be closed as it isn't summer. The "season" for everything being open is very much May to Sept here so while people recommending places like Rockport is nice, there won't be much open.

Portland Maine, Providence, Rhode island and Salem are all good train trips from Boston and have plenty to do. FYI the trains are very slow here so expect it to take longer than driving; Portland is a 2.5 hour train trip for less than 100 miles. You could also get a bus to Portsmouth, NH which is one of my favourite places to go albeit not on a train line.

Expect cold weather although honestly December temps are often similar to the UK. Jan through March is when it gets very cold here.