I like to play Anivia mid lane.
Positives: With constant ranged stuns and unlimited potential to burst an enemy down with an E R E Q follow up and her W ability to keep them from escaping, I rarely find an opposing mid who is able to farm efficiently against her.
Combine her nasty focus potential with her uncanny potential to escape even some of the hardest focuses with W and her passive which allows her to revive herself and shes a force to be reckoned with being able to burst down enemies and escape throughout the majority of the game.
In addition to this I also find since i don't see her being played too often some players don't know how to handle her and I have won games against 'better' players in the mid by catching them off guard in the early game and keeping them locked out.
Disadvantages: Well although she is a solid mid lane hero she can have problems against champions with a lot of mobility who are able to consistently dodge her stun, e.g. Flizz. She is also susceptible to ganks from mobile junglers who can get over her wall easily when she tries to escape, but only those have strong bursts to counter her passive, a good example is jax. Although I rarely find it a problem, because of the consistency required, champions with long range such as Caitlyn can also cause a problem if they play defensively and stay out of Anivias Q range.
She also requires a great deal of practice to play to the point where you can use your Q skill shot to stun them consistently and use your wall to escape, trap, block and disrupt flash and up until that point she is weak.
Overall however i'd say hero positives outweigh her negatives and shes a 'rare' enough champion that only experienced players will know any sort of counter strategy.