J.R.
Another great place to meet other Moms besides the Zoo (which is such a fun place) is at the local playgrounds. Lots of Fall River Moms come down to Westport Main Road Playground (it's fenced in) to play until naptime! Also, there is a playgroup on Friday mornings at the Dartmouth YMCA (from 10-12). The cost is $3 per child or just $5 per family (at least it used to be -- I've been out of the loop!). The YMCA is in "deep" Dartmouth on the way to Padanaram Village, but the space is great (it's right next to Dartmouth Early Learning Center -- preschool/private). I hope this helps you out.
-J.