Oh, no....painting the rocks and grout black will only emphasize the bad parts of the fireplace and make it look even funkier. Definitely paint it all white. Then paint the rest of the room a soft off-white/tan, just barely enough to contrast with the white fireplace.

Beautiful room, except the fireplace is a bit dull and dated. Please Google image white painted brick fireplaces to see the huge difference. You can leave the stones as is because they might add some rustic, organic charm amongst the white. And since you have dark floors and white trim, it'll look amazing and is a cheap fix and update. Here is another example where red brick was painted white. There are 2 fireplace before & afters in this link of pics:

http://www.younghouselove.com/photo-gallery-2/our-first-house/

For ideas, check out "contemporary stone dining room" posted yesterday. They covered their brick fireplace and it looks really beautiful. If you're unable to redo the entire fireplace maybe have someone come in and remove those rocks and fill in with matching brick then paint all of the brick to modernize and brighten the space. You have a great space!