When we were first looking to buy a loft in the Leather District back in 2002, we went to an open house where the real estate agent explained that the neighborhood is located so conveniently to all sorts of transportation options and outlets that it was "stupid." Apart from the stupidity of saying "stupid" (a good friend of mine used to say that it's impossible not to sound stupid when you say "stupid," and I think he's right about that), the agent had a point. The LD is within easy walking distance of the red line at South Station and both the green line (Park Street) and the orange line (Downtown Crossing), not to mention the commuter rail and Amtrak, which are both at South Station. Onramps to 93S, 93N, and the Mass Pike are basically in the neighborhood as well, and the airport is a 15 minute drive at the most.
For a while, there weren't any good public transportation options to the South End (it's walkable, and about a 5-10 minute drive, but the subway doesn't go there), but now even that's changed. A few years back, the Silver Line started up, and that goes right down Washington Street in the South End. Up until a month ago, though, you had to walk either to Chinatown or the Medical Center or the Common to get the so-called SL5. All these stops are pretty close, a 10 minute walk at the most, but now, with the advent of the SL4, which stops right on Essex Street directly in front of South Station, there is essentially a direct South End-LD T route. You can use a basic T pass to ride the Silver Line; it's a totally comfortable bus; and as a bonus, there are always some bizarre characters to share your ride with.