FYI, the first four episodes were announced to have following names:

Leavetaking
Shadow's Waiting
A Place of Safety
The Dragon Reborn

So that suggests Shadar Logoth featuring prominently in episode 2, while episode 4 might already contain the finale of tEotW. I'm a little unsure on what exactly 'a place of safety' might refer to - Caemlyn, perhaps. I've read elsewhere that Logain's role is supposed to be magnified in the series, so you'd expect some significant screentime for Rand's stay in Caemlyn in order to introduce Logain and Elayne.

Then again, it might also be possible that the Dragon Reborn episode title primarily refers to Logain, covering the Caemlyn stay, and that hence it takes several episodes more to get to the end of the book. But even then, it probably wouldn't take until episode 10 (or 12, or whatever number - but seems likely it wouldn't be much more than that).