I've never stayed at this bed-and-breakfast, but you can see from the photos that it looks pretty cute. I can tell you that the area is super quaint. Old Greenwich has a sweet, old-fashioned downtown with great little shops. The beach area is fantastic for walking and exploring with children. It's nice to get away from all the Greenwich snobbery, and this area is one of the best places for that.
Go here for more info on the Inn:
http://hhinn.com/