Where ever Nynaeve goes the pattern changes to death, riots and war. It started after Tear, First Tanchico, Samara, Ebou Dar.

im sure the list goes on 

No, Nyneave is not an evil taveren.

Tear, Tanchico and Ebou Dar all show what happens when the Forsaken succeed in manipulating those locations and in all but one case, Rand was not present to trigger a confrontation that exposed them, until much later. In fact, in all cases, Nyneave was always almost caught by them, especially Moghedien, which had heavy consequences for her later on.

The fact that Nyneave was present when those events occurred is what we call "coincidence." All those events were well on their way to happening anyway.

 

The Aiel had been over the Dragonwall for months, before finally arriving in Tear (likely pulled in by Rand's presence).

 

Tanchico was being manipulated by both Moghedian and the Seanchan before Nyn even stepped foot in the city.

Samara was a powderkeg under the oppressive hand of the Prophet.

And Ebou Dar was only the next step for the Seanchan after Toman Head, Arad Doman, Tarabon, and Amadicia.

 

Everything would have happened more-or-less the same way if Nyneave wasn't there.