I am playing Cassio since S4 and I must say, Zhonya is the biggest noob-trap on this champion. Cassioepia revolves around mobility and positioning and there are very very few situations when you can use Zhonya's active which makes you lose your mobility. It's better to run scaling armor runes and as 6th item run something other than Zhonya. Against hard AD you would rather to have Omen as 6th item (yes, Omen - you heard it right).
Core is on point - RoA, Rylai and Seraph's Embrace is a must. In 4th and 5th item you buy you usually want to have Rabadon's and one of those two: Void Staff or Abyssal Scepter (depending whether they have AP nukes or not). 6th item can be also the remaining item from those two, but in that time you already have 1000AP and it is better to increase your safety by buying stuff like Omen, Frozen Heart (very strong in many matches).
I would recommend you play some more games with Cassiopeia and see it yourself how strong itemization I put here is, as Cassio is mid/late game champion.
See you on Fields of Justice!