How does Nick meet Tom's mistress in The Great Gatsby?
Tom expressly invites Nick along on a trip to New York City so that he can meet Myrtle, his mistress. This trip takes place in the novel's second chapter.
On the way to the city Tom and Nick stop at Wilson's garage.
Tom and Nick arrive at the auto garage of George Wilson. Wilson and Tom exchange comments about a car Tom may sell. Tom arranges for Wilson’s wife Myrtle to take the next train to New York for a romantic tryst.
It is no accident that Tom introduces Nick to Myrtle. He goes out of his way to demonstrate his life-style and his adultery to Nick. We can see this as "showing off" and it is indicative of Tom's personality. Not only is he unashamed of the fact that he is cheating on his wife (Nick's cousin), he is down-right proud of the power he has over Myrtle and he wants Nick to know all about it.
To answer this question, take a look at the beginning of chapter 2. It is a Sunday afternoon and Nick is traveling into the city with Tom Buchanan.
As the train rumbles through the Valley of Ashes, Tom tells Nick that they are getting off because he wants to introduce "his girl." You'll note that Nick has not expressed any interest in meeting Tom's mistress up to this point. Arguably, this is because Nick is rather disgusted by Tom's infidelity. After all, Tom's wife, Daisy, is Nick's cousin.
After getting off the train, Tom takes Nick to Wilson's garage where they meet Myrtle, Tom's mistress. In private, Tom says to Myrtle that he wants to see her and instructs her to get on the next train. The group then head into the city to Tom and Myrtle's apartment.