Emma's Quilt Cupboard is awesome.. I have been there a few times.
You can take the commuter train from South Station and The Franklin train stop is right across the street from the quilt shop. Fun easy way to get there if you dont want to drive.
We used to have a really nice one in Quincy, but it closed this spring.
There is no quilt shop "in" Boston directly. There is a Fabric Store called Windmill fabric but to me the quality of the fabric is not good.
There is also Button Box Quilt Shop in Wellsley Ma that is really nice.
Most of the shops Sandi mentioned are public transportation accessable. Mostly Buses.