OK, good news/caveats here:
a) Best for-kids-and-adults food place: "Full Moon" restaurant in Huron Village.
Take the Red Line to Harvard Square, then grab a cab and have it take you up to the Huron Village area, (not far, should be under $8.00) where the fun-for-children-and-good-for-parents gourmet place is. (there are a couple of buses, but they would take a certain level of finesse, too stressful to try on a short visit.)
They have paper tablecloths with crayons, a play area, hot dogs, mac/n/cheese, PBJ, etc. for kids and REALLY, really good food for adults as well.
http://www.fullmoonrestaurant.com/Brunch is especially good--thick French toast...OK, I'd better stop thinking about that now...!
While you're there, (if you go in the daytime) there is the Bryn Mawr used bookstore across the street in one direction, and "Henry the Bear's Park" (game/bookstore) in the other. Also a Merimekko shop down the street and a Formaggio's Kitchen (cheeses, wines, etc.) a block from there.
Worth a couple hours' visit, at least, and you could couple it with Harvard Square following.
b) Other Activities:
In Harvard Square, there are two children's bookstores to visit, very near each other.
1) "Curious George" has all ages, including tiny kids' stuff, with a small play area, and for older kids a second section downstairs. Very worth the visit, it was begun when M. Rey was still alive, with her input.
http://www.curiousg.com/2) The Harvard Coop is across the street, and has a children's book section with play area in the basement, and they offer activities in the afternoons a couple times a week or so.
http://harvardcoopbooks.bncollege.com/webapp/wcs/stores/servlet/BNCBHomePage?catalogId=10001&storeId=52084&langId=-1At the bottom right side is a calendar listing the events for the month, with the kid's activities included.
3) If you do part of the Freedom trail or go to the Lexington/Concord area (Lexington Green, Minuteman park), check the National Parks Service tours and activities, many of which have some component for children.
4) Many local libraries have children's events, and the Boston Public Library is also in Copley Square, check their site for storytelling, etc.
5) In the Copley Square area, too: the Prudential/Westin Mall has a couple of kids-related stores (there's a Warner Bros' shop, and a California Pizza Kitchen that's kid-friendly, with a Cheesecake Factory on the lower level, opposite the Collonnade Hotel entry), and a huge Shaw's market across the street, if you are wanting to do snack-milk-other shopping.
Sadly, the FAO Schwartz store went away a bit ago, so the big bronze bear was moved to the Children's Hospital area. (Ditto the large bronze Donald Duck in Faneuil Hall, after a child fell off and the family sued, I believe...)
6) In the Lechmere area: Near the Museum of Science (up two blocks, over two) is a large, three-decker mall with a lagoon outside and several children's= related shops, a very good food court, and a Borders bookstore with a well-set-up children's area and cafe nearby.
But....all that said:
a) Echoing everything said above, and more--people are not mean to kids, but there is definitely less cooing and thinking they're cute when they are making noise, than (say) one might be if used to another region (like, maybe, the midwest, where I was raised) where the family thing is more common.
There is a higher percentage of singles in the area, most people are fairly serious when they're out and about (many more people use public transportation, either don't have or don't use their cars, and are working on the way to work, etc., or having business-like-meetings over meals, so there really is less tolerance for a lot of noise.)
They're not going to come glowering over you or anything like that if your child starts crying, of course. But there is a palpable difference in the degree to which the "children..seen, not heard" and "being expected to be little adults" thing is fairly long (say, 300 years or so) entrenched, and it's not likely to change soon. It sounds like that is less of an issue here, but you would want to be aware of it in advance.
b) The weather is also chillier and damper as winter approaches, so lots of layers and a cover-over for a stroller are a necessity. Also, re: strollers, if you plan to use the subways and buses, you will have to have a foldable, umbrella-like stroller, not one of the ones that looks like a child-sized VW bug with a bottle holder.
You are required to fold the stroller and hold the child for safety purposes, (aisles are narrow, fill quickly, and people push in and out) and people around you will get upset even if the driver doesn't say anything about it.
c) Is there any child care available in the hotel during the conference, or is your nanny doing that the whole time? That's a lot of hours solo with a little one, and the facilities for changing diapers and doing regular feedings are not always there when you want them in public places.
You might want to think about either having an 'extra' extra-pair-of-hands for at least part of the time, since it is a high-stress place (subways are not always well-marked, people don't often know where they are or how to give directions, most of them are visitors, too...).
And, if English is not the nanny's first language, people are not always as patient as they ought to be with that, either. (And direction-giving is truly horrible. Few cartesian-grid areas exist, and no-one knows street names beyond the two that border their house and maybe the one their office faces.)
I would also echo the questioning about the wisdom overall; if the child is breastfeeding, then I can follow why you'd be bringing her/him along, certainly, but if not, it might be a lot of work and planning and expense without so much gain for you or the nanny, really.
She'll be toting a kid all around a town that's not easy to get around in, can be expensive just for basics, and could (frankly) have a better "people-person" attitude at times.
The child won't really be able to take so much in that being in that town at that time would be so much different from doing similar things--bookstores, libraries, etc.--at home.
The "Make Way for Ducklings" ducks are good for about a 1/2 hour max: after you've sat on one or two of them, and gotten a picture taken with Mama Duck, that's about it (also they're out-of-doors, so if the weather is bad, that's not much fun, either).
It's nice to walk around the Public Garden (and the Cheers' Bar is nearby, go upstairs, not downstairs, for lunch...) and maybe stroll up Charles St. to look in the windows of the antique shops...but again, those border on things that adults would enjoy but children wouldn't really "get."
With some planning it could be worked out but there are things to be aware of in advance that might really not be so obvious...good luck.
