NoNewTaleToTell: It's the law across Skyrim (including Imperial controlled cities) that Khajiit (associated with caravans) are banned from cities. Argonians are free to live in Windhelm but choose not to due to the Dunmer (Dunmer and Argonians do not get along due to Dunmer doing Dunmer things in the past like enslaving the Argonians, taking their lands/etc/etc). It's confirmed by one of the Argonian dock workers in Windhelm (and in lore books). Also, if you're a Dunmer and you talk to the Dunmer who is being hassled when you first enter Windhelm she'll make a very rude (and completely out of the blue) comment about the Argonians. As far as the gray quarter, at least two elves (an Altmer and a Dunmer) in Windhelm say that the Dunmer more or less choose to live in the gray quarter and that it isn't as bad as the Dunmer there claim.
The reason why some Nords dislike the Dunmer is because they were taken in and given homes (and presumably were given help to start their businesses) after the Red Mountain incident and despite that, the Dunmer still consider themselves better than the Nords. Plus some Nords are actually just mad that the Dunmer won't join their side in the war. Oh, and the Nord that is worried about the Dunmer ends up as Jarl in Windhelm if you choose the Imperials which means he may just be trying to get their support for future need.
....Why the heck do I even know all of this?!
Ok so you two are obviously huge fans of Skyrim, why should someone who loved Morrowind and was slightly unimpressed with Oblivion (despite Sir Patrick Stewart, Sean Bean, and Terrence Stamp all doing voices!) finally get into this game?
Despite my occasional whining about the shallowness of Skyrim at times, Skyrim is a nice world to explore, gameplay itself (outside of magic) is improved compared to Oblivion, level scaling has been err....scaled back a bit so you will encounter enemies that are weaker and stronger than you and bandits aren't wearing Daedric armor. It also has some new legitimately interesting lore (although the main story ignores most of the lore, oh Bethesda). It's a better action game too, melee has a bit of weight for once and the classes are mostly balanced. The dungeons are improved over Oblivion's, though they're still linear (now featuring a new Dungeon Boss Room Escape Door (TM) ) but they at least have some size to them now.
Oh, and mods haha. Just to describe a few I'm using, I have one that adds somewhere around a hundred new unique fully voiced NPCs, a mod that makes you quite aware of the weather around you, a mod that adds around a hundred new lore-friendly spells and I just completed a three or four hour long fan made full length fully voiced DLC that takes place on a new landmass. It's rather annoying to hear (at least from those that constantly say "Mods will fix it!") but you really can mod Skyrim to your liking, it has thousands of mods.
