After an exhaustive search we have found a winner of the
"BEST FOUNTAIN PARK IN BOSTON"
it's actually in East Boston ("Eastie" to the locals).
Bremen St. Park was the clear winner and here's why:
-It has the address right in the name.
-Has the most water fountains with the biggest area
-The park is HUGE and divided into age levels
-There is tons of parking (except for 1&4th Wednesdays for street cleaning)
-You can eat lunch right there inside the park (this is unique)
-Speaking of lunch they have free lunch from 11-noon for kids (provided by the YMCA)
-It is right on the blue line and you basically step off the train and into the water.
-There are 4-5 police officers supervising the park (which can be good or bad but better safe than sorry)
The only "con" is that it IS in East Boston, not the nicest part of town and to avoid a toll on the way back you have to take the long way around. But It's worth it I think.