Boston Children's Hospital is accessible by car, bus or subway. For those who wish to take public transportation (The MBTA or just "The T"), the Blue line stops at the airport (shuttle buses run from each terminal to the T stop).
The MBTA trip planning site is particularly useful in choosing which subway trains and/or buses to take. Just enter "Logan Airport" and "300 Longwood Ave" (address of Children's Hospital) in the boxes where addresses are requested.
For those who drive, parking garages are available at each institution.