Free Japanese Audiobooks
An excellent list of free Japanese audiobooks can be found on this page (external site).
Kokoro by Soseki Natsume is my personal favorite of those listed, but as it is an older work, the grammar and kanji can be difficult. It's not as bad as you might think, though, because there is lots of furigana and the writing style is academic, which makes it easier for modern students to understand.
Personally, I recommend waiting to dive into audiobooks until your Japanese is good enough to simply listen to the Japanese and read along with the text. Many people recommend reading English along with the Japanese side-by-side, but this is not a very effective way to immerse oneself in Japanese. The simultaneous texts approach is good for translation practice, but when you have English available, your mind is likely to stay in "English mode," preventing you from processing the Japanese grammar naturally.