OK, after reading all these posts, let me put in my 2 cents on the Boston stations, and I write this as a current resident of Boston, who uses transit everyday.
Back Bay Station is a modern era building that is more spartan in design, but functions well.
You have a staffed Amtrak ticket window (it was closed for a brief time earlier this year), and a decent sized waiting room.
BBY has an Orange Line station as part of it and that allows for a direct connection to North Station, and the Blue Line for service to Logan Airport.
BBY is close to the Hynes Convention Center, many hotels, Copley Square, and the Newbury Street/Prudential Center/Copley Place retail district.
BBY has some basic shops including Dunkin Dounuts, and a great burger joint, Tasty Burger, that opened this past summer.
South Station is the historic "main" station that was rebuilt in the 1980's and is one of Amtrak's best (if not the best) big city stations.
BOS has a Club Acela, staffed ticket office, red cap service, and a checked baggage room, albeit you only have 2 trains that offer baggage service,
the Lake Shore Limited, and the last NEC train of the day, that used to be known as the Night Owl. You can also check baggage for the day there.
BOS is close to the rapidly growing Seaport District, home to the huge Boston Convention Center, and a number of hotels.
BOS is at the foot of the downtown crossing/financial district/chinatown/leather stocking areas, that are fast becoming as residential as they are business elated.
BOS has a Red Line station within it, and Silver Line service to the Seaport area, and Logan Airport (although I recommend the Blue Line for Logan).
BOS has many retail and dining options.
Route 128 Station, planned by the former New Haven Railroad, as a park and ride lot station, is now home to the rapidly growing "edge" city, and does offer
close proximity to budget hotels, popular in the same vein as the Braintree Red Line station that offers a number of modest priced chain hotels.
As for hotels, any hotel within the HUB can be pricey, book early.
The HUB refers to greater central Boston (back bay, copley, downtown, etc).
Most of all enjoy your visit, Boston has one of the fastest growing populations of major US cities, and has much to offer.
Ken