Man, I can ramble a good bit on different itemizations on her if you're building tanky.
To sum up, my build pool looks like this:
Mana -

Fairly standard, admittedly. Mana isn't something you can just skip on anivia. I highly favor building both tear and rod it gives a sizable chunk of HP/AP with strong synergies for a few defensive items I build on her.
Armor -


I strongly favor building Frozen heart on her as a tank, it synergizes well with her ultimate and it gives even more AP when paired with tear. Zhonya is a typical AP vs AD powerbuy. I don't buy randuins often, as it's a purely defensive item that doesn't double to provide me any offensive stats, but it's a lifesaver versus the vaynes and dravens of this world. Thornmail for people I know clearly aren't paying attention to my build.
MR -

Athene's also falls into this category. Abyssal can be useful, but the aura requires you to be a bit too close for comfort for me personally. Aegis can literally go either way. If you're a team player pick Locket to counter burst in teamfights, if you want to create pressure on the map/more gold for yourself, go Banner. Banshee's is nice to prevent you from getting locked down so you can't do your job.
Situational/Flex -


These items I buy under very specific circumstances or am in the process of experimenting with (namely sheen items). I'd give a blurb about each of them but it'd be about as long as the post so far. I do not buy rylai's on anivia, as I find that the major selling point of rylai's is lost on her, as all of her abilities slow to begin with.