"The eyes of Dr. T.J. Eckleburg" are a huge billboard that looms over the road right at the edge of the valley of ashes, near the garage owned by George Wilson.
The scene in which Dr. T.J. Eckleburg is introduced is a surreal one. Nick describes the valley of ashes as if it were an otherworldly, hellish realm. He does not explain where the ashes come from (in fact it was a large trash-burning operation), though he hints that the area is industrial with his descriptions of railroad bridges and workmen coming and going.
Similarly, Nick describes Dr. T.J. Eckleburg in a disorienting way. He tells us that the eyes of Dr. TJE are not attached to a face, but that they are huge, overlooking everything. We are left to conclude that this is a billboard. We are not told how Nick knows the name of the owner of the eyes (it must say so on the sign).
Dr. TJE's eyes hang over that part of the valley of ashes, unblinking and apparently all-seeing, like God. They observe the tragedy that is sown, sprouts, and comes to fruition at George Wilson's garage.
See the link below for actual photos of the place described by Nick, where a sign factory still stands today.