Damn! I had just finished writing a lengthy response for you guys, when my internet quit on me and I lost everything!
Long story short, as someone who used to live in the city I definitely recommend the subway as a way to get around. It's pretty clean, safe, a lot simpler to navigate than 90% of the subway systems out there, while at times it shows its age at the oldest system in the country, it's very efficient.
I also wanted to add, that for those of you who haven't been to Boston since 2001, the city has a changed a lot, and for the better! They got rid of the old elevated highway that used to run along the garden and moved it underground. They've replaced it with lots of park space and new developments so it just feels a lot cleaner and way more pleasant to be in that neighborhood.
It also means even more bars and restaurants have opened up and it's WAY more pleasant to walk to places like The North End, Faneuil Hall etc...
The Seaport is on of Boston emerging neighborhoods. There are some great new restaurants very near the BCEC and also some good shopping too like LouisBoston. Also the Institute of Contemporary Art opened a big, really cool space in the neighborhood that cantilevers over the harbor. DEfinitely worth checking out.
So with that said, getting to the venues early and eating grabbing a bite in the neighborhoods is a real possibility and a good idea.
When the weather is nice, it's actually a really nice walk from The Garden to The Seaport. But I would only recommend that if there's good weather out, which is rare in January.
So with that said the one weakness of the subway system is it closes pretty early. The last trains leaves at 12:15 so it probably hits North Station around 12:20ish.
I myself won't be there. It was either go home for Christmas or Nationals but I hope everyone has a great time! I'm definitely going to try to make it out for Worlds in 2015. That's too good an opportunity to pass up!