I personally think that everything from mid 2012 onwards is canon. This includes Jayce ruining Viktor's day, Darius and Draven being awesome, Varus murdering Noxians, Diana murdering the Solari elders, Rengar and Kha'Zix's rivalry, Nami's quest,, Vi's partnership with Caitlyn, Zed and the Order of Shadows, Syndra being a cocky bint, all the Shadow Isles related stuff and everything in 2013 and 2014. That's just me. It's pretty much safe to say that everything that's followed since the announcement of the Institute not being a thing anymore is totally canon, and considering they've actually said they were sitting on that decision for a while, it's reasonable to assume there was a lot of stuff made before hand with the idea that the institute wasn't canon in mind.
To help discern stuff, try and look at champions and see what would really change if the institute was never canon. If the answer is bugger all, then I'd say it's a safe bet that it'll remain that way, but these things get blurrier the further back you go, which is why I put my limit at mid 2012. Then it enters the realm of champions who may get changed, some more severely than others depending on the circumstances. For instance despite coming out at similar times, Nautilus is likely to get a lot more redone about him than Ziggs, since the League actually had a major effect on Nautilus, where as Ziggs's lore could have the institute removed and it would be just as good, minus a sentence or two.
or 
and those are the ones who are not canon anymore