If I were going to the Hyatt, I'd do exactly as Vttraveler says -- Silver Line to South Station, then walk. Way easier than a shuttle bus to the Blue Line, transfer from Blue to Orange, then walk from Chinatown station. But -- and this is a major BUT -- the walking route from South Station to the Hyatt is very much non-obvious -- very easy to get lost, and don't count on people being able to give good directions to the Hyatt. Way better to take a taxi from South Station, or, for that matter, a taxi from the airport to the Hyatt.

That said, the Hyatt isn't the most pleasant location for a 1-night trip to Boston, unless you were doing something specific in the immediate area. A place in the Back Bay or the Waterfront, while surely more expensive, would be in a far more welcoming neighborhood.