The highest item level chest armor a level 51–60 character can wear as a Warrior start with Bonescythe Breastplate (item level 92, epic). 190 items fit the slot and band; the top 25 are ranked here by item level, then quality, not by simulation.
Ranked by item level, then quality, among items with a known source: gear nothing drops, sells, rewards or makes yet (raids not yet open, the client's test items) is left out. The class filter keeps what the class can equip at level 60 (armor type, weapon skill, Dual Wield, the item's own class limit); the side filter drops items that only the other side's vendors and quests offer. Source: the best known drop first (a Forever rate at 10+ loots, else the vanilla 1.12 chance), then vendors, quest rewards and the profession that makes it. Reviewed picks: Warrior Best in Slot.
Other slots: Head, Shoulder, Back, Wrist, Hands, Waist, Legs, Feet. Every slot and level.