Flying Options
Saint John Airport
This is the closest airport with a 20-minute drive to Uptown Saint John. It's a regional airport, so there won't be any direct flights from Alberta. There will be connecting flights in either Toronto or Montreal. The total travel time from Edmonton is usually around 8-10hours.
West Jet Does not fly into Saint John.
Fredericton Airport
60 Min Drive to Uptown SJ
This airport is a lot like Saint John; it's a small regional airport that can't accept large planes, so you will need to get a connection flight from Toronto or Montreal. The flight times are roughly the same as those of Saint John.
Air Canada and West Jet Service this Airport
Moncton Airport
1Hr 30 Min Drive to Uptown SJ
This is the largest airport in New Brunswick, but it will still require a connecting flight if you're coming from Alberta. There are a few more options for flight carriers through this airport, so if you're looking at some low-cost options like Flair, this might be the better airport.
Halifax Airport
3Hrs 30 Min Drive to Uptown SJ
This is the only airport with direct flights from Alberta in the Maritimes. If you're looking at doing some sightseeing in Nova Scotia while you're visiting, this is the airport you'll probably want to fly into. The direct flights from AB are around 4-5hrs so even with the 3.5hr drive from Halifax, you'll avoid any potential flight delays while getting your connecting flights. The Digby Ferry is another option while driving back; it goes from Digby Nova Scotia to Saint John and cuts across the Bay of Fundy.
(I'll add that to the things to do section).