I also find it funny that noone's stated that though there is tons to love about Boston, you're going to be working more near Burlington than Boston.
Burlington will be your closest mall/shopping area: movie theatre, great restaurants (I suggest Rainforest Cafe and the Cheesecake Factory). It's a fabulous area. Close by is Lexington, which is fun to visit on a day trip, since it's got a lot of history about the American Revolution. I don't remember exactly when it is, but they do recreate Paul Revere's Midnight Ride (and yes, in the middle of the night).
As for the MBTA, you'll be able to get on the commuter rail in Woburn at the Anderson RTC stop on the Lowell line. Please keep in mind that the Commuter Rail is not the T and runs much less frequently than the T itself. Your best bet to jump on the T will be Alewife station in Cambridge, on the Red Line (though you can jump on the Orange and the Green lines....the Lechmere/Science Park end of the Green line has been in the throes of construction for quite some time, and thus I don't really know the status of it, and I much prefer my time on the Red Line than
any time spent on the Orange Line
) Alewife will be about 20 minutes south from you.
I lived in Wellesley for 4 years while I was at Babson, and worked over the breaks...I had a blast. I'm sure you will too
Feel free to PM me with more questions you may have.