Dude, you’re asking for it. Of course she’ll beg you to play her a song, because a man with a guitar is the universal panty dropper... but you probably already knew that, which is why your Martin is on display.
Your choice of wall art
This is arguably the most telling part of your room, since you are given a blank wall upon which to express yourself as you please. And you should use that space! No décor at all is serial-killer creepy, and/or the sign of a really boring human.
Posters procured from a sale at your college bookstore are all no-nos: the cliché beach scene, the Napoleon Dynamite movie poster, the two lipstick lesbians kissing in embrace. This tells her nothing about you or your interests, other than you’re too indolent to shop for real wall art. Photos of your high school basketball team mean you’re still basking in your glory days from more than a decade ago. Was that your life's peak?
A flag of the country you studied abroad in is great convo fodder if she also studied in Barcelona. But your parents probably paid for that semester of clubbing-and-sometimes-class, so if you still dub it "the best time of your life," she may wonder why you haven’t traveled further than that damn beer fridge since. Race medals and numbers say you’re a dedicated individual; but if you're rising at 7am for a training run, she's staying in bed.
Winning wall art: actual art, framed photos that you took yourself while skiing in Colorado (preferably demonstrating artistic talent), bookshelves with real books, and cool lighting. Now you'll get her attention.
Signed sports jersey
While a bit weird to have as a shrine (particularly if it's in a case), signed jerseys deliver cooler stories than a Peyton Manning poster taped over your bed. You may also gain some extra points if she allies with the same team. Otherwise, she'll be pissed when you ditch Sunday brunch with her to watch football with your buddies... every week.