Is there a Boston equivalent to NYC's Sweetiepie?
I would like to take my toddler and her friends out for a Saturday afternoon treat. I would love to take her to a place like Sweetiepie's. http://www.sweetiepierestaurant.com/
Wow! That is a really beautiful space. I don't think you will find anything with quite that level of design concept in Boston, but one place that has a similar aesthetic on a (much) smaller scale is Sweet Cupcakes in Harvard Square (though they do not have a lot of tables). I don't know if the Back Bay location has more seats, because I haven't been, but I do like their cupcakes a lot and imagine a toddler would too.
There is also a place called the Wenham Tea House, which I have never been to but which does have some vaguely similar menu items (perhaps it was the Sweetiepie of 100 years ago?):
Lastly, the most ice creamy ice cream shop I have been to in this area is Christina's, but the ice cream far outweighs the atmosphere there.
Granted you said Saturday, but maybe the Sunday tea at Upstairs on the Square? Funky decor, and kid-friendly treats.