The cone referenced is

Yoyogi-koen, as hinted at in the hint. This is in the bottom-left quadrant of the map along the green (Chiyoda) line, just above Shibuya, which is in large, bold text. Harajuku is nearby (to the right of Yoyogi).

Take two stations east along the

green (Chiyoda) line to Omote-sando, which is a station containing both the green (Chiyoda) and purple (Hanzomon) lines.

Two more stations along the purple (Hanzomon) line, one north-ish, one southeast-ish, and you're at

the Nagatacho station, the final answer.

The cone referenced is

Yoyogi-koen, as hinted at in the hint. This is in the bottom-left quadrant of the map along the green (Chiyoda) line, just above Shibuya, which is in large, bold text. Harajuku is nearby (to the right of Yoyogi).

Take two stations east along the

green (Chiyoda) line to Omote-sando, which is a station containing both the green (Chiyoda) and purple (Hanzomon) lines.

Continue along the purple line until

you reach the Hanzomon station, the only station to solely carry the purple (Hanzomon) line.

From there,

One station north (To Kudanshila) and one station southeast (along the light blue Tozai line, per your hint) leads us to the Takebashi station, the final station.