Roy, if you fix it, glue it or mend it via a shop or whatever, not only will it be expensive, but she'll know.
If my guitar had a crack, even a hairline fracture, I would be able to tell, changing pieces of it without telling her would probably end up with her being mad at you for not coming clean. If it were me in your shoes and I'd broken my girlfriends guitar (which she arguably loves more than me) then I would probably find out exactly how to repair it in the best way possible, and compare that price to getting her a better guitar.
Then I'd do one of the below.
1: Buy her a new one, get one of my artist friends who plays to do a beautiful design on it, something personal to us both or maybe her initials, fess up the breakage and take the crap that comes with it, but leave the new one as a surprise for her. I wouldn't be like "honey I broke your guitar but check out this baby!" because she'd feel that I didn't understand how important her old one was to her, I'd just leave it in her room and tell her downstairs, take the rap, then when she's done berating me (and probably having kicked me out while she cools off) she'd find the new one and realise that I truly wanted to make my mistake right.
or
2: Fess up to the breakage, tell her how it happened, take the crap, and give her the money and the details of where to get it fixed when she was more calm. Take the guitar to get repaired together to show that I do care and I'd apologise profusely the whole way through and if it couldn't be repaired at all in the end then I would just buy her a new one anyway regardless of whether or not she's still mad at me because at the end of the day if it had been mine she'd have probably wanted to do the same regardless of whether or not she could afford it.
Thats my advice, but either way come clean. if you reverse the situation and imagine that she'd done it to you than you'd probably be more mad at her for not being honest about what happened even if she did repair it behind your back than you would be for her coming clean and getting you a new better one/getting it repaired properly with you.
Good luck man, and remember, honesty is the best policy.
Peas