Katarina becomes more of an aoe mage without DFG.
Most builds have a few common core items, which are zhonya / void staff / liandry's torment or wizard hat / deathfire grasp / mpen boots / abyssal scepter. Let's assume your build is somewhere along the variety of this.
With this build, you are incredibly bursty. You have a lot of penetration and resistances, as well as damage. Without the active from DFG, you lose a considerable amount of burst which is just not replaceable. So, you can optimize for survivability or utility, because you have everything already for a full burst build.
Rylai's gives good utility and survivability whilst also being one of the highest AP items in the game. This would couple well with your resistances.
Twin Shadows gives utility, cooldown reduction, and a fair amount of ap. This item, I believe, keeps her previous assassin identity.
Will of the Ancients is another decent item that gives ap, cooldown reduction, and spell vamp. Alternatively, you could buy Hextech Gunblade. The active on it would be great for you.
There's also Banner of Command, Lich Bane, and Mejai's. None of those seem to be what you're looking for, though.
EDIT:
You could simply have both liandry's AND hat.