If I restrict to a narrow definition of public transit:
N: Badebakken, Oslo, Norway
E: either Greenlane or Ellerslie station, Auckland, New Zealand
S: Kelburn cable car station, Wellington, NZ
W: University of British Columbia, Vancouver, BC, Canada
A twist on that furtherest N, S, E, W you've been meme... the furtherest you've been using public transit (E/W determined by intl. date line).
Mine:
N: Copenhagen
S: Melbourne
E: Sydney (Brisbane if we count interstate trains)
W: Portland, OR