Flight
Other airports in the Boston-ish area are Manchester, NH (MHT) and Providence, RI (PVD). Each is ~1-2 hours away from the city by car with limited public transit options available, so we'd recommend Logan!
Train
Getting around Boston on the T is super easy and cheap. You can get a CharlieTicket or CharlieCard in most T stations and some convenience stores. Each ride is $2.40, but there are also multi-day passes available. Some stations (and buses) also have Tap-to-Pay. The station closest to the Wharf is the Aquarium Blue Line station. There are also multiple apps you can download to track schedules, see routes, etc. My favorites are ProximiT and CityMapper, but Google Maps also works well. If you'd rather skip transit altogether, Boston is also very walkable (and deceptively small).
Travel Note
Boston is hosting the World Cup this summer and there is a Scotland v Morocco game on Friday, June 19th at Gillette Stadium in Foxborough (~30-40 minutes southwest-ish of the city), which may impact hotel availability and pricing. If you need to stay further outside the city, we'd recommend staying West or North. If you stay near Waltham (to the West) or Salem (to the North), you may need to consider renting a car. Access to the green, orange, or blue line will be the easiest for access to the wharf if you won't be renting a car. If you have any questions about specific areas around the city, please reach out - we're happy to help!