The westernmost point you can drive to (with no ferries!) in NA is Anchor Point, AK. The Easternmost is St. Lewis, NL. The drive between the two looks pretty epic:
https://www.google.com/maps/dir/59.77329...6e16f!2m2!1d-55.6845142!2d52.3692011!3e0
Adding ferries, I suppose you can probably get from Unalaska to Cape Spear, via both Anchor Point and St. Lewis if you so desire:
https://www.google.com/maps/dir/53.82623...7af02!2m2!1d-52.6333333!2d47.5166667!3e0
In the other hemisphere, much more epic drives are possible (e.g. Dakar to Omsukchan, although getting to Omsukchan requires a ferry across the Aldan river, so not really ferry less!).
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