Use the tunnel from Union Station, as terenz described above, to go under Front Street directly to the Royal York, then turn left at
the end of the tunnel (lower level of Royal York, under the lobby), and walk to the end.
The airport buses are right outside. Give yourself at least 30 minutes to get to YYZ (longer if you are traveling in rush hour traffic--at least 45 minutes to one hour).
There are also airline limos parked at the bus loading area, if you so desire.
You can get to YYZ by subway and bus from Union Station, but this is very time consuming, as you would have to take the subway from Union to either Yorkdale or Islington bus stations, and then a bus from there--not your best option.

bj-21.

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'Tis better to have played and won, then never to have played at all.