I am a sucker for giving gifts. I like to have fun doing it.
What I would do is exchange gifts on Christmas Eve, or the day after Christmas. A day that the guitar store of choice will be open.
Have her open a pack of really nice guitar strings. make her think that is her gift. Be like, "I heard these are really, really nice strings. I cannot wait to hear you play them."
Wait like 10 minutes and make her sweat a little. Then lean back, stretch your arms and say, "well, lets go get you something to use with those new strings!"
Now for the important part. Call the guitar store today, like now, and let them know you are bringing her in to buy a guitar. Tell them your price range and situation. Have them pick as many guitars as they can that fit the bill and ask them to treat her really well when y'all come in the door. Make sure they know her name, etc. If they are a good shop, they will have fun and make her feel special.
She can play all the guitars and pick one out to take home.
That is more fun and she will get the axe that she wants.
If the store seems cool, have them remove the price tags so that she doesn't make her decision based on price. Obviously, you will tell her later on that she picked out the most expensive guitar in the store so that you will get a killer BJ.