Across all the games, which armor is your all time favourite for which race. Only choosing one per race.

For Dunmer it is Ordinator Armor (TES III: Morrowind) for me (Telvanni robes are close behind).
For an Imperial I loved Mithril (TES IV: Oblivion). I found it great for a spellsword / battlemage type of build.
For Redguard I love the new Hammerfell Garb. Make them more ethnic and unique.
For Nord I like the look of the Steelplate (TES V: Skyrim). I just wish it had a fur cape with it.
Altmer I like the Thalmor robes.

Khajiit: Ebony Mail/Armor. It's just so pretty!
Bosmer: Scaled armor
Argonian: Nightingale
Nord: Carved Nordic Armor!

For an Argonian i used to like Dreugh armor (Morrowind) as it was made from a creature that lives underwater and considering that Argonians can spend half their life underwater then it seemed an ideal choice. Plus it looked terrible on other races bur looked good on Argonians.

Nord: Nordic Trollborn

Dunmer: Chitin

Imperial: Templar

Argonian: Dreugh

Nords: Naked from Morrowind.

Imperial: The regular watch's armor from Oblivion.

Argonian: Dark brotherhood armor from Oblivion.

Orcs: Nordic steel armor from Skyrim.

High Elves: Thalmor robes from Skyrim.

Oh this is hard! I only play Argonians and I'm very picky... but I'd go with Argonians with Skyrim Elven. Just, that helmet.

The Argonian's kind of Mayan-style armour was actually one of the better things in ESO...