Maximum distance to station
Distance solution:
Python 3, 52 Bytes

return max(min(abs(l-c)for l in s)for c in range(n))

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Index solution (added after my first two comments):

Python 3, 59 bytes

return max((min(abs(l-c)for l in s),c)for c in range(n))[1]

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Edit: Switched back to Distance solution,
Thanks to Jonathan Allan for -1 Byte