How do I get into the Suhi High Roller in Lumoise City to start the post-game adventure? I thought beating the league was enough but I've done that 5 times and I still can't get in!
Its Lumiose City style, which is completely different than the style your clothing gives you. You have to max it to gain access (regular clothing style must be high too i believe). Lumiose style also gives you access to a bunch of other things, like new hairstyles and discounts to stores and cabs. Here is a list of things that up your style: http://www.serebii.net/xy/lumiosestyle.shtml
I believe the problem here is you aren't "stylish" enough. Style is a rating that gates various activities in Lumoise City. The easiest way to earn style is to buy Premier Balls one by one at the Pokemon mart somewhere in Lumoise. After ~150 with 0 style (less balls if you have mores style) the Mega Evolution stones in the stone emporium should be $10,000 instead of 10,000,000, and all "style" locked areas should be open.
If this is not the case, try beating the "Looker" subquests in Lumoise. I finished those and got max Style around the same time, so I'm unsure which triggered it, but for sure I can now battle in Sushi High Roller (spoiler alert: battles here are the same level as Cafe Le Wow but give lower rewards considering the price of "eating" there).
Ok so it may have to do with style but it does NOT have to be maxed out. The stone at the emporium still costs me 70k but i can get in to the restaurant. As for clothes, i'm not sure that has anything to do with it. I do have nice clothes from the boutique couture but...like i said idk. Anyway i think it mostly has to do with beating the league and having at least almost maxed style considering when they let you in, it's mentioned that it's due to you being the champion. If you're getting discounted cab rides, you should be good. :p
Edit: Also you do NOT have to do the looker missions. I haven't even talked to or seen the guy.
You do not need to complete the Looker missions in order to access the post-adventure. You need to have beaten the champion and have max Lumiose Style. Your clothing should be mostly comprised from things you can buy at Lumiose Boutique. You can tell when you have max style when music notes for boys and flowers for girls show up when it previews what you changed into.