I hope this doesn't ruin the thread before it starts by taking it in a bad direction (as it turns from "my secret base" into "the best bases I've found" removing the personal touch and making it competitive rather than fun)...bear in mind I'm European so don't have the game but stumbled upon this info as a result this is all untested. I imagine this thread might be a little slow for a while in any case (as many people will toy with these postgame, possible when more options are available).
It took a lot less time than I expected but there are QR codes for level 100 Blissey secret bases floating around. They might not be level 100 if you lack the level breaker item (found postgame...or maybe it is the base maker who needs the item).
Why does this matter? Level 100 Blissey is the most EXP you can get in the game by a long shot (and yes you do gain EXP from secret bases...maybe there is a setting to turn if off).
Assuming I did the maths correctly. The very minimum (using EXP all didn't take part in battle) is ~7000 per faint. But partaking in battle, having EXP O-power active at level 3, holding a lucky egg and >=2 hearts in amie brings that up to ~46,900 (you can even higher via traded and being above level when you evolve).
At that point you are getting above level 50 from just one fight with them (assuming 3) so it really is overkill (as competitive play sets your level to 50 anyway and Maison scales you down to 50 if above it and most Pokemon with moves at high levels also have them as level -- moves so can use the move reminder instead of grinding).
If you do use it you will learn to hate the level up jingle and it notifying you of each and every level up for each Pokemon in your team. Do bear in mind the Blissey might have healing wish too (makes Pokemon faint, next one sent out will be full HP and cured status) to make battles end quickly so a full team getting that much EXP might be impossible.
As a result that has potential to completely break the difficulty of the main adventure so don't use it during that. It might be an idea to instead bookmark this for whenever you find yourself in need getting to a high level quickly.
Examples (these might not be the best and I don't know if a QR codes are fixed or update to how the base is now or if there are other limitations on use...):
https://twitter.com/name_is_nama/status/536027797559336961
https://twitter.com/ginubz/status/536162150692040706
https://twitter.com/ginubz/status/535761869613461504
I'm sure a number of people will be making the same thing in due course if any of those are in locations of bases you have currently (if you don't mark a base as favorite it can overwrite existing ones without any warning*, you can never overwrite your own base)
*source:
http://www.reddit.com/r/SuperSecretBases/comments/2n1ui8/overlapping_bases/