They didn't even think of fixing the weather until after they found the bowl of winds and Elayne guessed that it had something to do with weather working.  Their original goal was to find something to convince the Salidar AS to tie themselves to Rand.  This is why Elayne lied later in the book and said she thought that the bowl required both men and women to make the bowl work properly.

In Lord of Chaos, in the chapter "Under the Dust", when Nynaeve and Elayne are using the need trick to find something to help Rand they first get taken to the White Tower in Tar Valon.  Nynaeve assumes that it is some kind of Ter'angreal, angreal, or Sa'angreal that they were getting to, but this isn't supported by anything else in the books.

Are there any theories out there as to what was in the tower that would have filled the need so well that it drew the super girls there first?  Something that would be kept either behind some barracks or a guardroom in what appears to be a cell?

I've got one theory, but it's not based on anything concrete.  Is it possible that the real Mazrim Taim is being held in that cell while somebody is impersonating him in the Black Tower?  Any other thoughts as to what could be in that cell?