Boston Logan International Airport: There is no sensible direct airport transfer to Rockport. Take the free Massport shuttle to Airport station, ride the MBTA Blue Line to Government Center, then walk about 10 minutes to North Station for the Newburyport/Rockport commuter rail. Allow roughly 2–2½ hours airport-to-Rockport once connections are included; the rail leg is about 70 minutes and was listed at $7.75 one-way, plus local MBTA fare. A rental car only starts making sense if Halibut Point and the wider Cape Ann coast are central to your plan.
Boston North Station: Take the MBTA Newburyport/Rockport Line train marked for Rockport; it is roughly 70 minutes. Rockport station is on Railroad Avenue, under a mile from Bearskin Neck and the harbor—an easy walk with light luggage, less pleasant in rain or with beach gear. Check the timetable carefully: this is commuter rail, not a turn-up-and-go metro.
By car via I-95 / Route 128 / Route 127: The practical driving approach is I-95 to Route 128, then Route 127. Do not count on finding downtown parking in summer: metered spaces are limited and often full. In June–October, use the free Blue Gate Parking Lot on Route 127, about three-quarters of a mile from downtown, then walk or take the $1 shuttle.