Just wondering if the trails are easily accessed by walking or public transport from St John's?
The trailheads at Quidi Vidi Village (Sugarloaf Path) and Fort Amherst (Deadmans Bay Path) are within the city. I walked from my hotel near King's Bridge Road to Quidi Vidi Village. The trail has a great website with lots of information that may help you. Trip Advisor won't let me post a link, but Google the East Coast Trail Association and you will find it.
No you would have to make arrangements. There is a Facebook group Hiking the East Coast Trail. Sometimes people live nearby and will provide a lift. Often you need a ride at the end of the segments because the trails don't loop back around. There are taxis but can get expensive.
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