Archmage

This is actually a REALLY cool feat for a wizard. Its powerful but not brokenly so given the earliest you could take it is level 8

It's pretty broken...being able to increase your Spell DC by 1 is generally saved for magic items or epic boons. A DC 20 on a spell save makes some creatures go from maybe being able to save against your spell eventually to never being able to save. Example: A Nightwalker will never be able to save against Wisdom saves and Intelligence saves with a 20 DC. It can't save from Int saves at 19 DC, but Int saves are fairly rare, but not being able to save against wisdom saves means that a single bestow curse completely nullifies the threat of a CR 20 monster.

Increasing a spellcaster's spell save DC is a homebrew faux pas. I'm surprised this has been voted as highly as it has. It's so powerful there's no reason every wizard wouldn't take this if it were an official feat.

EDIT: Currently, I believe the only way for a wizard to increase their spell save DC, other than increasing their Intelligence, is to find a legendary Robe of the Archmagi.

Mostly correct, had to search it out to find it myself. Max stat of 20 means only way besides the robe would be The Deck of Many things, a Wish spell,  a Tome. As for the dc, Arcane Grimoire only adds 1 while Robe of the Archmagi adds a monstrous 2.  Tomes have the added effect of also raising your maximum stat cap, which makes them much more powerful than a Wish, or the DoMTs. 

So if stacked with magical items one could reasonably without upping the stat above 20 have a +3 to dc for their spells...damn. Each of the items that do this is Very rare or legendary. Meaning the simple 1 from this feat is quite powerful, the plus one to the DC is equal to 2 in the required stat. Suggest to drop the int bonus and raise the level of this feat to require level 12, 16 or even 20 to make it fall in line with the strength it has.

This seems a little bit strong to me. I think every wizard will take this if available.