The first mention of the the eyes of Dr. T. J. Eckleburg is at the start of Chapter 2. When Tom brings Nick into the city and he meets Myrtle, Tom's mistress, Nick sees a part of New York that is completely unlike either East or West Egg, or the city of New York proper. Nick calls this middle place the "valley of ashes" because everything in this area is run-down place is covered in ashes -- it is an industrial waste land where everything is very bleak. In contrast to those images, Nick notices the eyes of Doctor T. J. Eckleburg. He provides the following description:
[The eyes] are blue and gigantic -- their retinas are one yard high. They look out of no face but, instead, from a pair of enormous yellow spectacles which pass over a nonexistent nose. Evidently some wild wag of an oculist set them there .. [and now they] brood on over the solemn dumping ground.
This enormous billboard, advertising for an eye doctor, looks out over the wasteland that is the valley of ashes. The billboard is located across the street from Wilson's garage, where Myrtle lives with her husband. The billboard is an interesting symbol because eyes usually represent sight, but these eyes are "blind," yet present -- perhaps a symbol that someone/God is watching everything. God sees Tom and Myrtle carrying on their affair. God knows what Daisy will do to Myrtle on this same piece of street when she races back from the city in chapter 7. The color of the billboard is also symbolic. Blue frequently represents dreams, but yellow frequently represents disease and decay, so the combination of the two implies that there are corrupt dreams here. That can be seen by all of the characters: Wilson wants more business and to achieve more wealth; Tom wants Myrtle; Myrtle wants a life-style that Wilson can't provide, but that she can pretend to have with Tom as his mistress. Nick's final comment in this chapter is that they walked under Doctor Eckleberg's persistent stare. To personify the billboard as if it would actually see clues the reader into the fact that those eyes are peculiar and potentially important.