I personally would like to see some kind of anthropomorphic wolf or something in the game. They seem to be rare in games (especially if you DON'T want an over sized brute, I would prefer something between Hyur and Miqote). Even though in the few MMOs I have played with them in it they seem to be fairly to highly popular and could be a draw for some people. If you want back story for them you could say they were enslaved by the Garlean Empire and their movement into Eorzea has given them a chance to escape and move into the city states of the land.
And Maybe even make a playable Moogle race. Basing their design on FFXII's design could make a fun character. And they would be a great draw for people who want to play as something that's cute and fluffy (darn you mogs and your quirky cuteness) as for lore: In times of crisis Moogles will take younger members of their race and using their incredible magical powers, change them into something that has a better chance at combat with the empire.
Another race I think would be interesting is a dragon man type race with scaled skin (with scale ridges and such), that are tall and have lanky limbs, yet still look powerful. Something that looks kinda scary and evil would be great for people who want a really dark and intimidating character. As for lore for them you could say they were for a long time held in the volcanic regions of the land by the Hellsguard Roegadyn who believe them to be some sort of evil (though their love for combat and killing doesn't help their case) With the new threat of the Empire the Hellsguard decide that they are a lesser evil and allow some free in exchange for their loyalty during the war.
I think these Ideas would be great additions to the game. And the more diversity and differences in the races the more people the game will interest. Their are many things that need fixing with the game but don't forget the improtance of having a character that you like. If you can't make a character you really bond with you lose a part of the game, a part that makes you come back to play it again and again.