My teacher said, she would let me pick a song I would play next. Right now, I'm on level 2 and I've been playing for 4 months. ._.

I just mastered Do-Re-Mi from the sound of Music which was Arranged by Eric Baumgartner.

I've never taken piano lessons, so I'm not sure what level 2 is like, but...

If you're looking for some rather easy anime music, you may want to look at Departure from Rurouni Kenshin, here on Ichigo's. It follows a pretty straightforward pattern throughout the entire piece, and it'll give you practice using both hands while playing.

Hope this helps. I've never taken lessons, though, so I'm not sure what level 2 is like. :\

Beaming Sunlight from Fullmetal Alchemist is pretty easy. you could give that one a go. :D

KH's Dearly Beloved. Its very easy and it can be found at ichigo's site.