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Rey had hunted for Luke Skywalker's location very hard, and has eventually found him. It seems clear from the answers to Why did Rey hand out Luke his blue lightsaber even if he had a green one after Episode V? that Rey wants to ask something from Luke.
What sort of help does Rey want from Luke? Does she want to be trained as a Jedi, and want Luke as a mentor? Or does she want to convince Luke to take a more active role in the rebellion, one where Luke joins the fight personally?
Rey's desire to find Luke has little or nothing to do with her own advancement as a Jedi. Her goal is simply to help the Rebellion. Later on, her goal seems to shift toward actively wanting to harm the First Order by denying them the map and bringing Luke back into the rebellion.
When Rey first meets Finn, she's deeply in love with the idea of the Rebel Alliance, having grown up in a community that's under the yoke of its own mini-dictator and living in the shadow of the Empire. She seems to have been raised on stories of the myths and legends of the Battle of Endor and Luke Skywalker and the noble activities of the Jedi Knights. When a couple of real rebels turns up on her doorstep and ask for her help, her immediate instinct is to follow them and help them, regardless of the fact that she's pledged herself to staying on the planet until her parents turn up.
“So you’re with the Resistance?” the young woman asked.
Finn glanced at the metal staff that could still club him unconscious. “Obviously,” he lied. “I’m with the Resistance…yes, I am.”
The young woman seemed to believe him. She swung her staff away from him to point at the droid. “Beebee-Ate says he’s on a secret mission. Says he needs to get back to the nearest Resistance base.”
At the end of the film, her motive seems largely to shift to carrying out Leia's orders to get Luke to come out of his self-indulgent sulk and rejoin the fight against the First Order
So intent were they on the current conversation and its possible ramifications that no one noticed that a light had come on atop a small R2 unit shoved back among the rest of the equipment in the room. Nor did they see that its hemispherical head had turned to look in their direction.
“We’re still at war with First Order,” Leia pointed out. “A war that won’t end until either it or the Resistance is destroyed. The next time, without Luke, we won’t stand a chance.”
Well, now that The Last Jedi was released, Rey herself answered your question. She gives two reasons to why seek Luke (SPOILERS):
Reason 1: The Resistance needs him. Leia hopes that Luke will help them defeat the First Order.
Reason 2: (Rey's real reason) She wants someone to help her understand how to deal with the Force, something she just found out was awoken inside of her.
Here's the transcript of Luke and Rey's conversation:
LUKE: Who are you?
REY: The Resistance sent me.
LUKE: They sent you? What's special about you? Where are you from?
REY: Nowhere.
LUKE: No one's from nowhere.
REY: Jakku.
LUKE: All right, that is pretty much nowhere. Why are you here, Rey, from nowhere?
REY: The Resistance sent me. We need your help. The First Order's become unstoppable.
LUKE: Why are you here?
REY: Something inside me has always been there. But now it's awake. And I'm afraid. I don't know what it is or what to do with it. And I need help.
LUKE: You need a teacher... I can't teach you.
Also, as seen in the previous film, and in this one, Rey grew up hearing about Luke Skywalker's myth. She looks up to him.
