This is how the game is laid out - if you look in the forest, to the
left is Alvina's hut (the buildings with the bridge in between), and her
butt basically faces Oolicile. If you take the elevator in her tower
down (in the past), you end up directly below. You can turn left, and
then left again, which leaves you with a 180-degree turn back so you're
facing toward the cliffside again (i.e. same way Alvina is facing).
Then, you take a REALLY LONG elevator downward, which seems to
approximately mirror the elevator in Darkroot Basin (visible in the map), but either way, you
more than likely end up in the Chasm of the Abyss, or...the VALLEY OF
THE DRAKES.
Given our map is at a fixed perspective, essentially
follow the map downward from Alvina's tower. Then, move right about
30-50 character paces, and then move downward again. That is where the
elevator leaves you off in the Chasm of the Abyss, or Valley of the
Drakes in the future).
[
Personally, I now believe that the Chasm of the Abyss was mostly the in the Valley of the Drakes, with more than likely some bleed over into New Londo, albeit mostly insignificant. HOWEVER, in the Chasm, there is a large bridge going diagonally downward, and I believe that this bridge leads you from Valley of the Drakes, not to the right into New Londo, but downward and into the Tomb of the Giants.
Tomb of the Giants wraps around New Londo, mostly going directly under it, and it makes sense that, at least one time, the TotG had access to the Abyss (which, truthfully, it makes sense that Primaeval Human would be buried in what the TotG used to be.
I could have taken more pictures, but really I just couldn't be bothered. I believe the map is pretty accurate, though, and these findings are merely what I believe to make the most sense, after experimenting with the map while simultaneously playing and switching between Royal Wood and Darkroot.