From the Wikipedia page (which also has a map marking the various entrances): "It can be reached through eleven entrances, five of which are accessible to people with disabilities. The wheelchair-accessible entrances, each with stairs and an elevator, are at Gansevoort, 14th, 16th, 23rd, and 30th Streets. Additional staircase-only entrances are located at 18th, 20th, 26th, and 28th Streets, and 11th Avenue. Street-level access is available at 34th Street via the Interim Walkway, which runs from 30th Street and 11th Avenue to 34th Street west of 11th Avenue." https://en.wikipedia.org/wiki/High_Line
There are access all the way. The start is at the south of the High Line.
I got on it near the Chelsea Market.
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