So, I talked to Karliah and she told me to go to Riften and meet her in the Ragged Flagon. The only issue is that every time I enter the doors to the Ratway, my game crashes. I can go anywhere else, but when I go there, Skyrim just closes instantly. I have no mods installed. Any ideas? I can't find anything about my particular problem because whenever I search, all I find are people with the issue of Karliah not showing up.

An alternative entry to the Ragged Flagon is available to any Thieve's Guild member.
Try the hidden entrance to the guild behind the Temple of Mara.
It looks like an above ground crypt.

Touch the Thieve's Guild mark on the stone coffin to open.

It's locked during the quest. It forces you to go through the Ratway.

You should try to look at windows events log. !!!!!!

----------------------

Have you the Unofficial patches installed - main game & DLC's (if you have them. !!!!)

Good idea, i'll check that out and post the results here if I can't find anything on my own.

EDIT: where can i find the logs in event viewer? I don't see any errors when i go to Windows Logs > Applications.