What is the quickest route to drive from Boston, MA to East Hampton,
NY possibly using a ferry from Rhode Island or Connecticut to Long
Island?  How much time would the ferry save compared to driving
through Manhattan? Thanks.

There is a ferry that goes between New London, CT and Orient Point, NY
that takes 1:20. The ferry runs every half hour.  More details can be
found at https://www.longislandferry.com/Default.asp

Total time that would be required (according to MapQuest) is 4:42. 
This appears to leave about 1/2 hour for the process of boarding and
getting off of the ferry.  Going entirely by car would take about
5:17.

The directions for how to drive, including using the ferry can be
found at:
http://www.mapquest.com/directions/main.adp?go=1&do=nw&ct=NA&1y=US&1a=&1p=&1c=boston&1s=ma&1z=&1ah=&2y=US&2a=&2p=&2c=east+hampton&2s=ny&2z=&2ah=&lr=2&x=63&y=13

Hope this helps.