I'd go for Capitol Hill, near Union Station. That's going to be a really nice environment for your child, and a short commute for you on the Red line. TBH I wouldn't want to stick your nanny and child all day in an apartment on Mass Ave or City Vista or whatever. Very few parks and other kid stuff. By closer to 2 you're going to want the kid in a part-time preschool program at least, and there's more of that on the Hill.
Plenty of new rentals being built up in the neighborhood. Check out Yarmouth Realty if you want to rent a whole house.
http://yarmouthm.com/listings/