Is there anything else that covers Itachi's story outside of the core anime and manga? I liked Itachi's character a lot and wanted to know more about him.

Are there any movies, or perhaps some light novels that cover more of his story?
The core anime and manga cover much of Itachi's story, particularly if you're only looking for his "canon" story. However, he does appear in other media.

As Abhishek Mishra says, he appears in the OVA "Sunny Side Battle!" Here is a list of non-core anime/manga media Itachi appears in:

OVA:


Hidden Leaf Village Grand Sports Festival! (as a cameo)
Sunny Side Battle!


Game:


Naruto Shippūden: Ultimate Ninja Storm Revolution--Ninja Escapades (OVAs within the game)


Novel:


Naruto Jinraiden: The Day the Wolf Howled (more Sasuke's reflection on Itachi's actions)
Itachi Shinden: Book of Bright Light/ Itachi Shinden: Book of Dark Night (related to Shippuden #451-458--this answer says it follows the novels, Naruto Wikia says it doesn't, I don't know enough to say either way)
Akatsuki Hiden: Evil Flowers in Full Bloom


Movie:


Road to Ninja: Naruto the Movie


Naruto Wikia has a list of all video games in which he's a playable character.