Now then...

For a long time, I have wanted a X360 for some of the Japanese goodness that it provides: Lost Odyssey, Infinite Undiscovery, a bunch of SHMUPs and so on. It has better versions of every 7th gen Armored Core, as well. 

That said, I was mostly a PS3 man during gen7, so there has to be a lot of stuff that I missed. What am I looking for is:

• Interesting Japanese games, preferably exclusive to X360 (or, having a signifcantly better version on it). I prefer JRPG's, but anything goes.
• Exclusive games in general, preferably of the sleeper hit nature.
• What's the best Halo game available on the platform, and does it have local co-op?
• Try to keep it to disc-based games, with PS4, Vita, and Steam, I really am set for downloadables.
• I have a half-decent PC, so if the same game exists on PC, I would prob rather play it there.
• ...honestly though, if you feel that it is good enough, whatever you can come up with is fine.

Thanks

OH.SHIT.

I've been a 360 expert ever since 2011.

Interesting Japanese Games :
Tales of Vesperia, Blue Dragon, Lost Odyssey(I'm assuming you didn't play it on Xbox One), Infinite Undiscovery, and these other ones aren't exclusive but maybe Eternal Sonata and Nier?

Keep in mind Fable is(surprisingly) one of the most popular RPGs of all time, so you might want to pick up Fable 1-2 if you are open to "western" RPGs.

Ok for real though when it comes to sleeper hit exclusive :
Dorito's.Crash.Course.2. Not even joking, this is such a fuuuuuuuuuuuuuuuuuun game. Try Perfect Dark Zero too, that's one of those rare games I think looks good but didn't get. Don't forget if you want Banjo Kazooie it's on the Xbox marketplace!

The best Halo is 3 but I think it's debatable that Reach is just as good of a co-op experience. Really you only need to bother with those 2 games, and if you're interested play Halo Anniversary's campaign.

Fable trilogy (you can finish them all in about the same time of the average JRPG.)
Lost Odyssey
Blue Dragon
Tales of Vesperia

There are many thoughts on what the best Halo campaign is. I'm partial to Halo 4, while many others would argue Reach and Halo 3. Any of them are notable split screen games though.

Also, the Gears series is great for split screen. That's four solid games there.

If you want SHUMPs, just look in the marketplace. There are a bunch of those in there varying from ports to original games.

All that could keep you busy for couple hundred hours.

Dead or Alive Xtreme 2, Rumble Roses XX and Onechanbara: Bikini Samurai Squad. Hey, you asked for exclusive, interesting japanese games

I've played a bit of Tales of Vesperia and it seems good.

Avoid Lost Odyssey, specially if you hate slow battle systems.

Gears of War games have local split-screen co-op (since you mentioned it when talking about Halo).

Somehow Deathsmiles (Cave) was released in the west.

The previous users have pretty much summarized well the games you should get.

· Lost Odyssey should be your top priority. After that, Tales of Vesperia, Nier (if you didn't play it on PS3, since it plays better on 360) and The Last Remnant. There's also Blue Dragon, Magna Carta 2 and Infinite Undiscovery, which aren't particulary engaging, but no harm in you giving them a try.

· There's a bunch of shumps that are extremely fun. My personal favourite is Akai Katana, but don't miss out Doddonpachi, Deathsmiles, Ikaruga and Radiant Silvergun. (Most of these can be found in the marketplace, but there's several physical versions available).

· Some strange japanese games, like Ketsui, Senko no Ronde, Culdcept Saga, Vampire Rain or Operation Darkness. These might be particulary hard to track (some were USA only), and I can't attest for their quality. It's worth giving them a shot, though.

· Best Halo available is Halo: CE Remastered. That being said, you can get yourself a copy of Halo 2 (for the OG Xbox) and it works like wonders on the 360, plus four-player splitscreen available to you right there. Might as well try all Halo games on 360, although I personally hate Reach.

· The Fable games; despite the first one being on PC, the third one is broken and can't be played anymore (GFWL), and the second always remained 360 exclusive. Second one is the best, so there's also that. It's not heavy on RPG mechanics or anything, but it's a fantastic and a charmer of a game.

· Gears of War is hella fun, probably the best flagship MS franchise on 360 (yeah, even better than Halo in my eyes). Even if the macho steroid hero bravado saving the world from ugly monsters isn't really your thing, just go ahead and give it a go. It's great in co-op (splitscreen), and has plenty of replay value and interesting extra modes.

· Project Sylpheed, to satisfy that need of a good Star Fox game that never came during the seventh gen. It's a short game, but very sweet, especially if you're into space combat.

· There's a bunch of extra games you could see yourself getting. Beautiful Katamari is fantastic, so go for that. Ace Combat 6, if that's your jam. Crackdown games are okay, I personally didn't like them, but they are fun for some people. The Diswasher (digital only) can prove to be engaging. But above all, don't miss out on Geometry Wars 2 (also digital-only); it's a fantastic game and extremely engaging, plus can allow up to four people playing it on the same screen. You don't even need to play the original one since this one is basically the original one but revamped, with more modes. Do yourself a favor and get this ASAP.

· Some Rare games, like Kameo: Element of Powers, or Perfect Dark Zero. They aren't particulary great, but can be enjoyed.

· Rumble Roses XX, Onechambara: Bikini Samurai Squad and Dead or Alive Xtreme 2, if you're feeling horny. Hey, there's tastes for everything!

· Some multiplatform games that were under the radar and performed better on 360, like Majin and the Forsaken Kingdom, Condemned (given that only 360 holds both titles of this franchise), and the likes.

EDIT: They were ported to everywhere else at this point, but goes without saying, the Dead Rising games. There's a Xbox 360-only collection that actually holds two titles (Case Zero and Case West) that are 360 exclusive, and you get over five fantastic games, probably among my favourites on 360. Get them too!

Pretty sure I've mentioned over 15 games, so you have plenty to work with already. Hope this is sort of what you were looking for.

Project Gotham Racing 3 and 4

Look at some of RARES older games like Banjo Kazooi: Nuts and Bolts, Perfect Dark: Zero, Kameo: Elements of Power, Viva Pinata... Solid games.
Can't forget: Crackdown, Fable 1, 2 and 3, Ninja Gaiden either.
In Fables case, Fable 2 was never on PC and was in my opinion the best game in the franchise, Fable 3 is no longer sold on Steam either.

If you are a Naruto fan you can't look past Naruto: The Broken Bond and Rise of a Ninja. Both Xbox 360 exclusives too. Sadly, due to Ubisoft's license expiring, those games ended up having their DLC removed.

Halo 3 was certainly the height of the series.
If you wish to play it for the Story... Getting Halo: Anniversary, Halo 2 (Backwards compatability with the Original Xbox means it works on the Xbox 360.), Halo 3 is a good place to start.

If you wish to see something more technically impressive that showed what the Xbox 360 could do when all the details were baked... Look no farther than Halo 4.

-Forza Horizon for one of the best racing games ever.

-Gears of War 1-3. The first is good but 2&3 are excellent. Too bad there aren't any other games in this series...

-Fable 2 was fantastic when there was an online community. Not sure if it holds up, anymore.

-Witcher 2 if you can stomach the learning curve.

-I really enjoyed Magna Carta 2 though it might not be for everyone.

Project Sylpheed is the first game you need to buy :)

Right. So, so far (for the close future), I have decided upon:

1) Halo 3
2) Lost Odyssey, IU
3) Ace Combat 6 (forgot that exists!) and Pro. Sylpheed.

SHUMPs, all mentioned I was aware of
Gears.. i will have to watch a lot of gameplay. It has frequently put me off by its macho nature, and considering it'd be a coop game for me my g/f, it's a touchy choice (even if hella cheap).

Keep 'em coming! Especially multiplats with the PS2 for example.