I'm arriving in Boston on the train from New York on July 4. I've booked accommodation at the YWCA Berkeley Residences.
I'd like to know where I will be when I get out of the train. Will it be far to the hostel?

You have a choice of two stations (both downtown). They're actually not that far apart from one another (walkable even).

the second last stop:

Boston Back Bay
145 Dartmouth Street
Boston, MA 02116

OR

the last stop:

Boston South Station
2 South Station
Summer Street & Atlantic Avenue
Boston, MA 02110

Have fun in Boston!

Back Bay Station is closer to YWCA - less than a half mile. Unless you have massive amounts of luggage, you could walk it.

Definitely Back Bay - much closer.

Sorry, I should have googled the exact location. Gail and yk are correct. Back Bay is much closer, walkable... but if you accidentally dozed and went to South Station, it would not be an expensive cab ride to the hostel.