In another question, it was quoted from the script that although Luke wanted to "walk away from everything", he specifically went searching for the First Jedi Temple as a "personal quest". What are his goals at this point?
Right now it's anybody's guess what the in-universe explanation is. But thematically, the entirety of Ep.7 is about trying to find a way home, full stop. The First Order is trying to "make the Empire great again!", Kylo Ren is obsessed with roleplaying as his grandfather, Leia is fervently trying to locate her brother whom she hasn't seen in years, Rey is irrationally determined to wait for her parents to come back, etc.
The sole exception to this pattern of past-oriented characters is of course Finn, who has no past to speak of. As the movie progresses, he seems to slowly start to regard his lack of a meaningful past as cause for sadness/regret, but likely we'll see later on that it's a source of strength of him because he's free to look forward in way no one else seems to be doing presently.
Also note the fate of the one character who succeeds in finding his way home:
Han's opening line is after all, "Chewie, we're home." His celebration is short lived.
Which brings us to Luke, the most Legendary protagonist of the saga. His disillusionment with the present is also arguably the keenest. In an episode so fixated on quests for one's origins and the secrets better-times-past, I think it's fitting that Luke would be driven into to the deep, deep past, on the border between history and myth.
There's no stone clad evidence to suggest why Luke was searching for the first Jedi temple yet. However there are theories flying around that there is an old powerful relic hidden there that will aid the Resistance in the battle against the First Order.
Other theories are Luke went into solitude to learn more about the force (much like his former master Yoda), and another theory that he couldn't deal with the fact that his nephew had turned on him, and he hid away because he was ashamed of his failings.
Alas, this is all conjecture, and we won't really know the truth until the second or third film in the trilogy. Maybe best to mark this question down as one that will possibly be answered fully, as late as 2019.
Let's recap what we know about the situation for sure (too many spoilers to wrap the whole thing)
- Luke started a Jedi academy at some point between the Vader BBQ and VII
- Leia and Han have Ben Solo, who, like his mother, is adept as using the Force (not necessarily after #1)
- Ben (just like Anakin/Vader) was an angst filled teen who gets sent to Uncle Luke's Jedi academy to hopefully temper it
- At some point Snoke gets ahold of Ben and turns him to the Dark Side, where he takes the name Kylo Ren and apparently is put in charge of a small Sith/Dark Side group called the Knights of Ren
- The Knights of Ren wipe out all of the Jedi at the Jedi academy (remember, Luke is referred to as the last of the Jedi in VII)
The rest is conjecture but I think (for an in-universe explanation) it fits pretty well, even with what little we know.
In ROTJ we see Luke and Obi Wan talk about Anakin and we see that, despite the decades, Obi Wan still regrets Anakin's fall. It was quite a blow to have an apprentice turn Sith, but to have someone you were close to betray you like that... It's quite a disturbing thing, even outside a movie.
We don't know how close Luke got to Ben Solo, but not only did all of his students die (or perhaps some of them turned with Ben), but his own nephew was the chief executioner. So how do you tell your sister that you not only failed to save her son, but now he's become as bad as your father ever was? (Even outside the Star Wars universe, Darth Vader is still one of the greatest villans of all time.) And who would want to train to be a Jedi now, knowing such a thing happened? No matter how you look at it, Luke failed as an instructor of the ways of the Jedi, just like his master, Obi Wan.
If I were Luke, I'd want answers before I started another academy up. Just starting up again without any consideration would likely only to turn out someone as bad, if not worse than Kylo Ren. Surely this happened before. How did the Jedi deal with it in the past? Is there a way to teach someone to be a Jedi that avoids the pitfalls Luke encountered? Or even some comforting words from a former master who failed in the same way.
It's highly likely that the Emperor had all the Jedi temples he knew about destroyed (we know the one on Coruscant was and if any others were known they'd be gone as well). So you'd have to go looking for a Jedi temple that wasn't well known. Moreover, the first temple would probably give some clues as to how to fight the Sith in general (Luke only faced 2 by himself, now there's considerably more). And, of course, there's the benefit of the fact that you're going to abandoned places not on the map (literally) so people who might want you dead can't find you easily.
Maybe the Jedi and Sith are just gone. link
Kylo Ren was not Vader's apprentice, he didn't go through the Sith path of murdering his master. Also, the idea of him being a Sith "Lord" is ridiculous. He's bordering on a Sith cosplayer.
But the same is true for Luke. The Jedi Order was a millenia of traditions and knowledge; how long was Luke on Dagobah, a month? What training that Yoda gave him can he pass on to his students, hitting them with sticks and balancing on their feet?
The Jedi and the Sith are gone. The Sith annihilated all trace of the Jedi, and Luke/Vader ended the lineage of the Sith.
Maybe Luke's going back to the origins to either recapture what was lost, or to decide what comes next.
My fan theory: I think these three films will at their core represent the Past, the Present and the Future. Awakens is obsessed with returning to home, the past, references to history. VIII will be about these new characters that we've grown to love. And IV will be "what will the galaxy become without these two iconic power structures that it was built around?"
Luke's reticence to once again engage might be because he thought he had already fought the "final" battle, only to be confronted again with a similar scenario. If you thought you had resolved the ultimate threat, only to discover this had created a worse threat partly of your own making, you would have to question your role in the genesis of the current situation and ponder your existence. Luke needed to get to a neutral state to examine his status.
Before Disney retconned all the books and other canon sources, there was a story about how Luke learned how to see the future like his father before him through the Force. Unlike his father Luke could control his flashes, and in one he learned that in order for the Force to return to balance he HAD to go dark side. There were reasons like to find and shut down emperor Palpatine's cloning factory.
In the movie I think he saw the future and saw that Rey would be needed to subdue the dark side and in order for her powers to awaken he had to leave, and Kylo Ren had to go dark. The Jedi order has prophecy out the wazoo in some of the ex-canon sources. The first temple probably has a lot of info, and just like the dark places on Korriban where contact can be made with dark lords. There are probably places in the first Jedi temple on Ahch-To (no not the sneeze...) where the same can be done with Jedi masters.
As for Kylo Ren, Luke must have told him and his other students about the dark side. Especially about his father Darth Vader, and must have told them about Darth Vader's redemption, Kylo probably idolizes his grandfather for the redemption, having to go dark himself for the good of the galaxy. Remember all those scenes where hes asking his grandfather for help, help to resist the pull of the light. To resist wanting to return to the light? To do the things that must be done?
None of this is canon or anything, just a lot of speculation from what I've read in previous materials. But I think it ties a lot of the unanswered questions together nicely.