I think the city would be incomplete without the DoH and DoL classes, so I'll give them some mention.

I think Mason would be an interesting DoH to add, along with more things conceivably made out of stone (mostly weapons, with some heavy armor, mats, and housing goods). This only fits in with Ishgard better than Gridania, but I think it could work. Unfortunately I don't know a whole lot else they could add for crafting, since we do have most the bases covered.

I saw this in the general discussion thread about Heavensward, but I think shepherd would be an interesting DoL that could fit with Ishgard (mainly thinking of the karukals). It could gather animal goods from conceivably tamed (or wild) animals, fleece, skins, meat, horns, etc. Most of those are currently available from mob drops, but the class shouldn't be totally redundant and should include things unique to gathering, finding a use for those things though.....

I would imagine most of the new classes added in the expansion will be placed in Ishgard (with the exception of musketeer), but they could have jobs elsewhere. For example, a katana wielding class could start in Ishgard, but then go to Limsa (or Mor Dhona for that matter) to get the samurai job. I do think that Dark Knight would start in Ishgard though. I've gotten a dark'n'unfriendly vibe from Ishgardians so far, so I think they'd go well together.