Who do you think will be the first Straw Hat that Tashigi will truly become friend with the first (not counting Zoro) ?
Nami with a bullet. They have the same general sensibilities, similar ages, and Nami respects Tashigi as is because she reminds her of her late mother whom she respected as a noble marine. Tashigi would also be intrigued by Nami's ability to sense weather patterns, as well as the work she puts into her world map. Plus Nami would tease Tashigi in being more feminine, but all in good fun.
Beyond her, I think she'd grow close to Chopper who is innocent and has a good head on his shoulders. He'd probably be the member, besides maybe Zoro, who'd be most interested in hearing her talk about swords.
I think she'd struggle getting use to Sanji, Franky, and Brook. Sanji's overbearing chivalry would rub her the wrong way, Franky is every boy's ideal and Tashigi showed complete disinterest in his antics, and Brook would likely freak her out the first time around. Though like everyone, she'd come around to them and consider them good friends.
Luffy and Usopp seem like guys she'd scold. Luffy for doing something reckless and stupid, and Usopp for lacking a bit of backbone.
Robin and Jinbe are the most mature members, so she'd appreciate their company right away, though I still wonder what Tashigi thinks about Robin. I like to believe she got over their encounter during Alabasta, but that was one of the most significant moments of character growth Tashigi experienced, and it was through the backdrop of being humiliated by Robin. I think she's grown past it and is more sure of herself, therefore accepting of Robin.