I live in Moncton NB, and can offer some ideas... Halifax Nova Scotia is probably going to be the first stop for the plane, as it is a connector point for international flights. Saint John (spelled out for the province of NB, as opposed to St. John's, Newfoundland -- might save confusion when booking flights), Fredericton, and Moncton are the closest Canadian airports. The coastline along the southern shore of NB from Saint John to St Stephen is gorgeous, however it can get a little nasty weather during the winter months. For transport, go to http://www.smtbus.com/ for the bus company that services New Brunswick and Nova Scotia.
if Delta must be the airline of choice (unsure if they fly into any of the above listed cities), it does fly into Bangor International Airport in Maine, which would be the closest location to the St Stephen area, and I believe that SMT Bus Lines actually has connectors running from Bangor too... good luck!