What incentives does Nick have for visiting the East Coast in Fitzgerald's The Great Gatsby?

What struck me about your question was the nuances behind the
word "visiting." Your question implies that Nick never intended to stay in the East, ... that he
fullly intended to move back home to the Midwest. In this regard, I don't agree. Nick was
escaping the Midwest and the trap of his "clan ... descended from the Dukes of Buccleuch." He
wanted to MOVE to the East and not simply visit.

That aside, let's
get to the meat of your question and look at his "incentives" from the text. Directly after Nick
mentions how trapped he feels by being in his particular family clan, Nick talks about his
great-uncle and his involvement in World War I. It is precicely his involvement in the military
that Nick says made himm "come back restless." He expands further to answer your question
directly:

Instead of
being the warm center of the world, the Middle West now seemed like the ragged edge of the
universe--so I decided to go East and learn the bond business, so I supposed it could support one
more single man.

There you go. The
charm of the Midwest has gone in the eyes of the more worldly just-back-from-the-war Nick. Most
likely, he is sick of being around the same "blah" people with solid values. Nick is looking for
something new, vibrant, a whole different way of life. Enter West Egg. Something new? I think so!
Yep, "solid values" sure do go out the window, don't they?

In
conclusion, the irony is that Nick ends up simply "visiting" the East, even thought that wasn't
his original intention. The East was too corrupt a place for little Midwestern Nick. He moved
back where he belonged, clan or not.