Getting here
Among the best-connected spots in New York, and slightly awkward to reach on foot from every one of those connections.
The Seaport sits at the bottom-east corner of Manhattan, tucked between the financial district and the East River, with the FDR Drive running along its edge.
Subway
Fulton Street is the station, and it is a large complex served by a great many lines — the 2, 3, 4, 5, A, C, J and Z all reach it. From the exits, walk east along Fulton Street, downhill, towards the water. It is about five to eight minutes.
The walk is the part people get wrong. Fulton Street runs a long way and the Seaport is at the very end of it; if you can still see office towers on both sides, keep going.
Wall Street (2, 3, or 4, 5) and Broad Street (J, Z) are alternatives from the south, slightly longer on foot.
Ferry
NYC Ferry stops at Pier 11 / Wall Street, a short walk south along the esplanade. Several routes call there, and arriving by water is by some distance the nicest approach.
The free Staten Island Ferry at Whitehall Terminal is about fifteen minutes' walk around the bottom of the island, along the esplanade past the Battery Maritime Building.
On foot and by bike
The Brooklyn Bridge pedestrian entrance is a few minutes north, which makes the Seaport a natural start or end point for walking the bridge. Coming off the bridge into Manhattan, walk south along the waterfront rather than through the traffic at City Hall.
The East River Greenway runs along the esplanade with a protected bike lane, connecting north towards the Lower East Side and south around the Battery. Citi Bike docks are plentiful.
Driving
Don't. The FDR runs directly overhead with no useful exit for the district, the streets are narrow and cobbled, and parking is scarce and expensive.