Three airports serve Boston — Boston Logan (BOS) is the main international gateway and closest to downtown; TF Green (PVD) in Providence is a strong secondary; Manchester (MHT) is northern New Hampshire's option. Most World Cup visitors will fly into Logan.
Boston Logan International (BOS) is the only major Boston airport — 4 mi northeast of downtown across the harbor and the closest jumbo gateway to Gillette Stadium (~27 mi south of the airport). Most international visitors arrive here. Logan has direct rail+bus transfer to downtown via the MBTA Silver Line.
All terminals are connected by the free Massport airport shuttle and inter-terminal walkways. Allow ~15 min between terminals on foot or via shuttle.
If domestic fares are significantly cheaper into PVD or MHT, here's what to expect. Both add travel time vs. Logan.