So now that GF has released the updated type chart, I bet they're just itching to show it off. There's no better way to do this than through the Gym Leaders and Elite 4, so here's the direction I think they'll take this time around. I'm also taking into account the starter matchups, since they either like to keep them equal or have each one represent a different level of difficulty.
Gym 1: Bug (Viola)
We already know that the first gym is in Santalune City, the first place you travel to, and it makes sense that it's beyond Santalune Forest. In addition to the gym design itself, Bug is a common early-game type, Vivillion serves as an ideal ace pokemon what with its "secret", and most importantly the type has been updated. It's been a while since grass has been the disadvantaged starter from the beginning, too.
Gym 2: Fairy (??)
I think that this, along with bug, has already been confirmed? In any case, those bug pokemon you caught may not turn out to be that useful here against this shiny new type. I could already see a few Fairy pokemon being available by this point (Flabébé, Dedenne, possibly Swirlix/Spritzee) and it would be a good way to introduce the type early on in the game. Notably, the abundance of fire-type pokemon makes it likely that you'll have some help against the gym in case you don't know about the type yet.
Gym 3: Electric (Clemont)
Clemont has already been introduced, and specializes in gadgets. Also, his gym has the bright lights / neon thing going on for it that Elesa's had in Gen 5, so I think it makes sense to put this here. GF has favored the early-game electric gym as the third badge in the past, too. It gives Froakie users a challenge, and I guess shows off Electric's new immunity to paralysis.
Gym 4: Rock (Grant)
With the reveal of Korina, I think this has become less ambiguous. His name, look, and gym design all imply the rock-type, which makes this the first time the type is used elsewhere than the first gym. It gives Froakie an advantage to make up for Gym 3, gives Chespin an advantage to make up for Gym 1, and bring Fennekin users to a disadvantage given its success in Gym 1, which balances everything out.
Gym 5: Fighting (Korina)
From her look and badge, I think it's pretty safe to say that this is a fighting-type gym. It is one of GF's favorite types to include (seriously, it has been an E4 or Gym type in every region, and was both in Gen 2), and it has also been impacted by the type chart. Furthermore, fighting's focus on raw power fits well with Korina's connection to Mega Evolution. And if past generations are anything to go by, it's around this time that your pokemon will be first reaching their final stages anyway.
Gym 6: Water (??)
So if I'm right about the first 5 gyms (which seems to be the case given the hints), I think Water will follow. We've already had three types that have been altered and you are already near the coast, so I think you'll head to the slightly southeastern city on the shore. Water would be perfect here, unless they decide to throw a curve ball. Assuming Chespin was Grass / Dark, the last gym was hard for it, so this throws it a bone. It does the opposite for the Fire / Psychic Fennekin.
Gym 7: Ice (??)
By now, I've assumed that traveling through the region starts in the southern central region, heads north to Lumiose, west to Shalour, and then south to Gym 6. Following some shenanigans with Team Flare, the protagonist heads to eastern Kalos, which is covered in Ice. It'd be illogical not to have an Ice-type specialist in the area and Ice has generally been either gym 7 or in the E4.
Gym 8: Dark (??)
Wrapping up the gyms, I think Dark will be the last type. I'm not sure what direction the story will take you, but Dark hasn't ever been a gym but has been in the Elite 4 three times. The typing tends to have decently powered attackers, few weaknesses, and gets to show off that type chart again. It's a better option than the other remaining types, IMO, with Psychic being the only real competition here. It helps Chespin's final evo out after having gone through an Ice gym and Fire gang, penalizes Fennekin just a bit for a nice balance, and let's Froakie go out with a bang given its general neutral position in the early game.
Assuming that they evolve by the 5th gym, that leaves:
Chespin with 3 weaknesses (4 if you count Team Flare) and 3 advantages.
Fennekin with 3 weaknesses and 3 advantages.
Froakie with 2 weaknesses and 3 advantages (4 if you count Team Flare).
Given the variation in weaknesses/resistances of each individual type and the pace of the games, I'd say that's as balanced as it will get. Psychic is another decent option for the 8th gym, leaving the starters with similar difficulty levels as well.
I'm not getting into the Elite Four too much, but I think it'll consist of Poison, Ground, Steel, and Dragon in no particular order.