Aviendha certainly gets closer to Elayne, but I'm talking about Siuan, Leane and the Wise Ones.

You certainly cannot argue Egwene didn't become a close friend of Siuan and vice versa. There's no reasonable reading of their interactions, let alone their own words, that can come to a contrary conclusion.

Same for Leane, whom Egwene visits pretty much ever night despite being beaten multiple times and exhausted from being Healed and the physical labor she has to do.

As for the Wise Ones, especially for Amys, Egwene's own thoughts indicate something much deeper than friendship. She says she thinks of Amys like her mother, and that certainly seems to be borne our by their relationship.

But with Melanie and Bair, there's certainly deep friendship. Melaine planned to name her daughter after Egwene, and while most of the scenes of the 4 of them enjoying each other's company is implied as the scene fades to black, there's really no way to ignore that they're very friendly.

Or I guess there is a way to ignore all that...