Bradley Airport (BDL)
The closest airport is Bradley International Airport. Bradley is served by American, Delta, Southwest, and United, along with a number of regional airlines. It is located about 20 miles north of the city. A shuttle is available to downtown Hartford: http://www.bradleyairport.com/transport/public/
Amtrak service is available to Hartford.
Bus service from NYC and Boston is also available via Peter Pan and Greyhound.
From Union Station to the Cathedral
The shuttle from the airport and the bus and train, all arrive at Union Station in Hartford, which is just a short walk from the Hotel or Christ Church Cathedral. See map below.