I've read up to volume 11 of the manga of A Certain Scientific Railgun and volume 5 of the manga of A Certain Magical Index. As of volume 5 of Index, the manga has not caught up to the conclusion of the anime. For Railgun, the Sisters Arc concludes in volume 7. A new arc also begins in volume 7, so that's the one you'll want to start with that, chapter 40, called Clique.
Going back to Index, only the first seven volumes have been published in English. Despite not having read two of them, I'm fairly confident that none of them passes the point the anime got to just by looking at the covers and reading summaries. From the Wiki page, I would guess you would start at volume 17 for the Index manga since the second arc involving the Catholic nuns ends in 16.
I didn't recognize the Academy City Invasion Arc at first since it's been a while since I watched the anime, but it appears this arc was in the anime. Volume 17 is the latest Index volume and it covers this arc. So, I have to change my conclusion.
As a side note, none of the A Certain Scientific Accelerator manga has been animated, so if you need to know where to start at that one, it would just be the first volume.
- A Certain Magical Index Manga: volume ? (as of volume 17, it doesn't appear that the manga has passed the anime)
- A Certain Scientific Railgun Manga: volume 7
- A Certain Scientific Accelerator Manga: volume 1