M.C.
Hi K.,
My family and I have always enjoyed the "blue park," Friendship Place, in Berlin. It is located at Willard Elementary School on Norton Road. It is part of the "Boundless Playgrounds" project (www.boundlessplaygrounds.org)which includes accomodations for children with differing abilities.
In New Britain itself, the playground at Stanley Quarter Park has always been fun. My sister and I used to play there as little girls and I still take my kids there today from time to time. Also if you guys get the urge, Stanley Quarter has a path which winds around the pond. You can always take a break and stroll her around the water to look at the ducks, frogs, etc.
Feel free to bring your baby over any time, too, if you'd like some company; my sons (2 and 4) are always looking for playmates :)
--M.