Reddit mentions of The Amulet of Samarkand (The Bartimaeus Trilogy, Book 1)

You seem to have two types of books here, fantasy YA and classics that span the genres.

For fantasy YA-type books I recommend:

1. The Monster Blood Tattoo series by D.M. Cornish.
   
   
2. The Bartimaeus Trilogy by Jonathon Stroud.
   
   
3. The 3 volumes of the Chronicles of Chrestomanci by Diana Wynne Jones.
   
   
4. The Discworld Series by Terry Pratchett. It's not technically YA but would be very complimentary to YA, I think. The books are mostly standalone, though set in the same universe, so you can start anywhere. I started with "Small Gods," and it was great, so I recommend it as an entry to Discworld.
   
   
5. The Abhorsen trilogy by Garth Nix.
   
   For non-YA I think you might enjoy from the other books you've included, I recommend:
   
   
6. Watership Down by Richard Adams
   
   
7. The Hobbit/Lord of the Rings by Tolkien
   
   
8. Since you're interested in Sherlock Holmes, I wonder if you might be interested in The Beekeeper's Apprentice by Laurie R. King. It's the first in a set of novels reimagining Sherlock Holmes after his retirement, when he takes on a young woman named Mary Russell--his match in intellect and observation--as a protege. I first read The Beekeeper's Apprentice at about your age and loved it.

http://www.amazon.com/The-Emperors-Soul-Brandon-Sanderson/dp/1616960922

Should be good for her.

http://www.amazon.com/Brightly-Woven-Alexandra-Bracken/dp/1606842102

Little more romancy. Surprisingly not awful.

http://www.amazon.com/Amulet-Samarkand-Bartimaeus-Trilogy-Book/dp/0786852550/ref=sr_1_5?s=books&ie=UTF8&qid=1377613887&sr=1-5&keywords=jonathan+stroud

While she is not exactly the main character, the female lead in the Bartimaeus books is definitely the strongest character.

If you're looking for YA Fantasy I'd suggest The Abhorsen Trilogy by Garth Nix, His Dark Materials by Phillip Pullman, or The Bartimaeus Trilogy by Jonathan Stroud. All three series managed to recapture the magic that Harry Potter had for me. Other than that I'll just reenforce what everyone else is going to say in Game of Thrones, Ender's Game, Name of the Wind, and Dresden Files.

The Bartimaeus Trilogy?

I was a fan of The Bartimaeus Trilogy.
http://www.amazon.com/Amulet-Samarkand-Bartimaeus-Trilogy-Book/dp/0786852550

I definitely want to recommend one I just finished: Hard-Boiled Wonderland and The End of The World. Without spoiling anything, think along the lines of Inception. Absolutely one of the best books I've ever read.

If you enjoyed The Hunger Games, you'll probably like The Bartimaeus Trilogy (this links to book 1). Has a more Harry Potter feeling to it but the humor is so well done. Really fun read.

I think there was a book about Zeus bowling or Hera dancing or something along those lines...

EDIT: In all seriousness though, has anyone else read the Bartimeus trilogy? Harry Potter-esque fantasy stuff, but there was an interesting dynamic that I picked up on that runs throughout the entire trilogy: the government is completely run by magicians, who can work magic and are perceived as "better" than "commoners". Yet, over the course of time, people slowly become immune to the effects of the magicians' (or, more specifically, the demons they summon) magic, and thus revolutions continually occur as the commoners rise up to overthrow the magicians (government). In the end, it turns out that, with the proper drive and schooling, ANYONE can become a magician, a fact not widely known.

The parallels are interesting, and include ministries of propaganda, unpopular foreign wars, and hidden groups of subversives who conspire to overthrow the government - all of this in the "background" of the story, which primarily focuses on secret plots and magical exploits, again much like Harry Potter.

I'd be interested if any other AnCaps have read these and picked up on some of the same stuff. Audio books are great too, read magnificently by Simon Jones.

The Bartimaeus Trilogy?

Bartimaeus Trilogy - Jonathon Stroud

SO good. Mystical Creatures and beings combined. Plus runes. You will love it.