For my own reference: what Kaito thinks of Johto and how he feels about the Pokemon adventure/the kidnapping/the fact he can't get home/etc. This is stuff that really mostly happens behind the scenes in his mind, away from actual logs and threads and stuff like that (though occasionally it comes out into the open). But it's good for me to write it down so I remember where I'm coming from with him! Feeeeeeel free to skip!
AUGUST 10TH NOTE: I AM IN THE PROCESS OF UPDATING THIS. Since things have changed and such. Stay tuned for a new essay *A*
So Kaito has been in Johto a good three months now, and generally, he's handling it pretty decently. He's a very adaptive person, so the transition wasn't too difficult for him, even if getting used to... fire-breathing and electricity-producing mutated monsters took some time (but it would take time for anyone so). In general, he likes it here. He thinks the Pokemon training thing is actually kind of fun, and he's fairly decent at it too because he's a quick learner, so picking up on the ins and outs of training (such as type weaknesses, abilities, items, and other strategies to use during battle) was a cinch for him. He may not have played the Pokemon video game at home, but in a lot of ways, he can tell this world is fashioned after one. Kaito was a pretty big gamer in his own world, so he's very familiar with certain video game formulas. He recognizes all the signs of a classic RPG (such as NPCs who haunt the same places seemingly 24/7, randomly scattered items across the world, a fairly linear travel pattern, etc etc) and his adaptive nature allows him to slip into this formula easily. He's also finding that, for a video game world, Johto is actually really big, and he's never really bored because there's always something for him to do here. The only things he doesn't really like about Johto itself is the law enforcement (he finds the system even more incompetent here than he did at home, only because he has yet to meet police officers/high school detectives he begrudgingly respects and can have friendly rivalries with) and the ghost-Pokemon events (like the nightmares and the kidnapping to Sprout Tower). He's aware that it isn't necessarily the safest world (especially not after Kay's kidnapping and him meeting Joker and Vanitas's post to the network), but it's generally peaceful and he likes that! He means it when he says it isn't so bad here once you get used to it, because in his mind, it really isn't. Things could be a whole lot worse, and hey man, Johto can be super fun.
Unfortunately, one huge huge huge factor that keeps him from enjoying Johto and the Pokemon adventure to its fullest, and that's the fact that... he was basically kidnapped here.
Although he doesn't mention it often because it never really comes up, this is something he has absolutely not forgotten, and it definitely paints Johto in a more cynical light in his eyes. As per a conversation with Heather quite some time ago, he's acknowledged the possibility that the whole 'happy aura' of this world could very easily be a front, and the 'Pokemon Adventure' could be a ruse to distract everyone while whoever brought them here does... something evil (though he honestly has no educated guesses on what that something evil would be). This puts him on high alert (not stressed or tense alert, but wary nonetheless) and, though he might not be a detective, he's been actively searching for clues and other hints that might inform him of a way home. He explores every city/route as much as he can, from inch to inch, and makes mental maps of each one as he passes through (you never know when knowledge of a certain terrain/area would come in useful, after all). He doesn't really write this stuff down though because that's just not his style, and he has a pretty good memory so it's easy for him to keep up with things. Kaito really... doesn't like the idea that he's been kidnapped either, because it means he's at the will of whomever brought him here, and he's never been the type of guy to play by anyone's rules but his own. The fact that he's been here three months and a) hasn't found a way home and b) hasn't managed to find out who brought him here bothers him much more than he lets on, because 'lol if I can't find out what's going on here how the heck am I going to get home?'
Which brings me to the fact that Kaito... really, really wants to go home. He has a lot of unfinished business back in Ekoda, what with his father's murderers still at large and Pandora's location still unknown. The longer he spends in Johto, the more time his dad's killers have to search for Pandora without his interference, and the idea that they reach the gem before he does fills him with dread. Yes, he's observed that this world likes to mess with timelines and bring people from the past/future and things like that, but he isn't convinced this means that time doesn't pass normally at home compared to Johto. When he goes back (it's a when for him, not an if) months might have passed in Ekoda, and that is Not Good. This fear remains a very large driving force in him wanting (and trying as hard as he can) to go home.
Naturally, this desire causes juuuust a bit of conflict for him in terms of Johto CR. In three months, he's managed to make quite a few close friends that he's already started to trust in ways he's never trusted people before. Kaito is a pretty closed off person (poker face at work, here, plus the idea that he has to shoulder the whole KAITOU KID thing on his own because a) he doesn't want to get anyone else involved in the danger that is his job, and b) a good part of Kid is done for revenge on his father) but meeting someone who could empathize with his story so thoroughly (i.e. Kay) has kind of taught him that there are a few people out there he can talk to about his situation (though it helps they aren't from his world, because it means there's less liability in telling them about Kid). Making close friends in Johto is a problem for him, because when he goes home, he knows they can't come with him, and he knows there's a pretty big chance he'll never see them again. Regardless of this fact, Kaitou Kid > everything else in Kaito's life, and though he certainly, honestly and truly, cares about the people he's met here, if he found a way to go home, he would take it :( It wouldn't be easy for him at all, and there would be a lot of INNER ANGST AND STRUGGLE and he'd probably throw a few cheesy lines of 'I'LL NEVER FORGET YOU GUYS' toward Kay and Johan and everyone else in an attempt to hide how much leaving them would bug him (and he'd probably try to bring his Pokemon with him at this point ahaha), buuut... yeah. His mission is the most important thing in his life, his duty to his father transcends EVERYTHING (even in canon, he chooses to continue heisting as Kid even though he sees how much it hurts Aoko and her father) and it's not something he would give up so easily. It's a very selfish part of him :(
So how is Kaito remaining connected to home, despite the fact that he is throwing himself into the Pokemon training thing head first and willingly? I already mentioned that he's writing letters to various people (such as his mom and Aoko and Jii and Inspector Nakamori and probably a mocking one to Hakuba from Kid's point of view just to mock him 'hur hur can't catch me Tantei-san~' and stuff like that). To clarify, Kaito isn't really homesick (though he, like anyone would, misses his family and friends). His adaptive nature generally prevents him from getting homesick, so he isn't pining for home 24/7 or anything like that. The letters are written sporadically and infrequently, and they serve as small reminders that, although he's having fun in Johto, he has something to look forward to and a mission to complete somewhere else.
TO REITERATE: he is having fun in Johto. Truly and honestly! And this is why you don't see him talking about going home too much, because he can hide all of this wariness and desire to go home behind a cheerful exterior and genuine playfulness as far as the Pokemon are concerned. Poker face also prevents him from expressing what bugs him too. His dad emphasized the fact that Kaito should smile, no matter how upset he was feeling, so even when things are bothering him he'll just keep on smiling and joking and dorking on.
Also, a small note on Johto + Kid: Kaito is pretty convinced Pandora isn't here, on this world (why would it be?). So even though his main motivation for heisting has been taken away, he hasn't... heisted in three months. Heisting isn't an addiction for him or anything (thought he has fun with heists and loves the adrenaline rush and the intellectual challenge of outsmarting the police force), but he knows he's going to have to continue heisting when he goes home. The last thing he wants to do is let his skills get rusty, so it's very likely he'll host a heist or two while on Johto. Especially now that he's in Goldenrod, which is so similar to Tokyo. The only thing that'll make his heists not quite worth it is the lack of high school detectives trying to stop him (h-he'd miss the challenge, honestly).