If you have some sort of Massport badge (even a temporary, escort-only badge) you probably can use the Terminal B parking garage. Just make sure you have it and that it's visible. If anyone questions you just flash the badge and they'll probably leave you alone.
If they do ask you to leave try Constitution Beach in East Boston. It's easily accessible via the T. Take the Blue Line to Orient Heights station. When you get out walk up to the main road that crosses the tracks. Cross that street. You'll see a small triangle and a liquor store on your left. Walk down that street (Barnes St). The entrance to the beach is a block down. That's good for shots when 22R and L are in use for take offs. For snapping landing shots instead of continuing down Barnes St turn left onto Baywater and continue until you are at a desired angle for approaching aircraft. Generally when this runway config is in use 27 is the principle arrival runway with 22L being used as a secondary runway and 22R as the principle departure runway. There is a park further down into Winthrop that is good for getting arriving traffic onto 27 but I only know how to get there by instinct and not by traffic signs (which are HORRIBLE in Massachusetts anyway).
Fort Independence, locally known as Castle Island is another excellent off-airport sight. It's right across the entrance to the Inner Harbour in South Boston and has very good views of approaching aircraft onto 4R and L. It's a bit further away when take-offs are on 22R and L but it's still incredible to sit up on the hill and watch a Heavy start rolling down the runway, then lift off and slowly climb out over you. Although with most of the older 747-100/200s, 727s, DC-9s, L-1011s, and DC-10s gone, the slow climbs and deep rumbling in your chest are all but a thing of the past. While the A330s, 747-400s, and 777s are still very cool, a bit of the effect is missing.
One place that is long gone but definitely one of my favourites was the old Satellite Parking Lot. It was situated just to the right of the threshold for runway 15R. While take-offs aren't extremely common and landings very rare, there were a few times I was able to enjoy it.
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