Even though it’s aimed at a female demographic, I can’t really recommend Yo-Jin-Bo. When I was playing it, I got the distinct impression that it was a gender-swapped moege along the lines of To Heart or Da Capo, with the tsundere / kuudere / genki-girl / yandere stereotypes simply being replaced by their cooler male counterparts. Sure, there’s an ongoing narrative with life-or-death stakes, but the structure is very formulaic and the story is shallow and kinda boring despite the fanservice. The decision tree is practically identical on every route, so there really isn’t much incentive to get every ending - the journey is the same almost every time.
I could recommend Animamundi as a good female-oriented visual novel because of its strong narrative and atmosphere. On the other hand, I won’t endorse a game that’s been censored to Hell and back (literally). That said, I can’t really advise buying Animamundi, or, to a lesser extent, Family Project.
I agree with papillon’s reservations about Kira Kira. Like I said earlier, Deardrops is easily the better of the two - great characters; sympathetic, charismatic lead; nice art; good music. Sure, Kanade looks like a palette-swapped Yui (K-On!), but her character is anything but. Even the characters that I’m not that fond of, I still like to a certain degree.
I wouldn’t recommend Yume Miru Kusuri unless you’re certain that your girl is comfortable with sexual content. My biggest complaint about the title was that the sex was fairly gratuitous. The narrative is quite strong, but the sex in some cases is decidedly unnecessary. Kana was written by the same author as Yume Miru; I won’t say that one is better than the other, but I have no problem underscoring that Kana is the more accessible of the two by a large margin.
As mentioned before, moege titles could potentially backfire on you by alienating those you were trying to win over, so I wouldn’t recommend any of the Da Capo or To Heart titles, or (as much as it pains me to say this) even Shuffle or Edelweiss. A title with a strong story and likeable characters will fare far better with your girl than one with only the latter.
Cogwheel Country, Sunflower Girl (Sharin no Kuni, Himawari no Shoujo) is a great introduction to visual novels, but you’ll probably have a hard time finding it. PaletWeb has three copies of the game in stock (used, here and here for $89.99 and new, here, for $104.99 - you must register for an account to bypass the age gate). Like Fate, I think it’s worth the investment - I own both the original and its fandisc, Children of Eternity (Yukyu no Shonenshojo), as well as its follow-up, The Devil on G-String.
Tsukihime and Fate are from the same author, but good luck finding a copy of the former. I think the characters and narrative themes are much stronger in Fate; the higher production values and easier accessibility make it pretty one-sided as to which I’d recommend over the other. Still, Tsukihime is supposedly being remade and re-released, so, if the translation patch is modified to support this version, I’d recommend it as well.
I haven’t played Growlanser or Sakura Wars, so I’ll have to reserve my judgement on those two even though I own the former (my copy is still sealed). On principle, though, I think these are more RPG/VN hybrids rather than pure visual novels - if we’re throwing hybrids into the mix, I may as well mention any title in the Fire Emblem series and Aselia the Eternal (I haven’t played either of them yet, so I can’t endorse them just yet, but I’ve heard great things about them).
I almost forgot to mention the visual novels that already have mainstream releases. The Ace Attorney series, Time Hollow, Jake Hunter: Detective Story, Nine Hours, Nine Persons, Nine Doors, Trace Memory, Hotel Dusk: Room 215, and Snatcher are all worth checking out. All of these are console titles and thus have no sexual content in them, so if you have a Nintendo DS or Sega CD, there’s no need to restrict yourself to PC releases. The story mode of the BlazBlue series is also presented in visual novel format, so there’s a possibility that she’s already played a few VNs and simply not realize it.
I hope this has been helpful.