In-game dialogue states that Argonians are not allowed in the cities, but there is an Argonian barkeeper in Riften. It has also come to my attention that Khajiit are not tolerated within a city's walls. Are only the caravans prohibited? Would a Khajiit born in Skyrim and assimilated into the Imperial culture be able to live in a city? .Also, which cities are the two races not allowed in and which are? Why? Any clarification would be most welcome.

*sets out tea and cookies*

I imagine you're referring to the part about either Jaree-Ra in Solitude or the Argonians of Windhelm in your first part. Jaree-Ra is a known criminal, which is why the guards don't like him. In Windhelm, the Argonians live on the docks because it's A ) The only place they can afford to live and B ) The Nords would probably treat them worse than the Dark Elves if they lived within the walls.

And generally, the Nords don't seem to care at all if a non-Nord was born and raised in Skyrim, they only see another race and ostracize them. A few dark elves will say they were born and raised in Skyrim but they're still treated poorly because the Nords just see outsiders. A Khajiit born and raised in Skyrim would also probably get a lot of hate from the Nords because, again, they just see a cat and not a Nord.

I think some NPC's will say that Nords have a genereal distrust of Khajiit due to their reputation as thieves.

The Khajiit caravans are not allowed in any city. Some of them will say that it's because they're suspected of being smugglers and thieves. Other Khajiit appear to be allowed in, because you can see one or two Thalmor agents in towns.

According to an Argonian on the docks at Windhelm, it was Ulfric who made the policy that Argonians were not allowed into that city. If you side with the empire, the new jarl, Brunwulf Free-Winter, says he's not allowing them in because the Nords in the city don't want them there and it's for their safety. It could also be because there is a large Dunmer population and Black Marsh invaded Morrowind after Vvardenfell.

Windhelm is the only place with a ban on Argonians, but the executioner in Solitude complains about Jaree-Ra and says "a lizard like him wouldn't have been let in when Torygg was king." So there may have been a ban there at one time. Some Argonians are miners in the smaller settlements. One Stormcloak jarl (Sorli the Builder, who takes over in Morthal after a Stormcloak victory) has an Argonian in her household staff.

AFAIK there's no problem for a Khajiit or Argonian PC or follower anywhere.

I use to feel sorry for the Khajiit Caravan back then but after spending some time with them, and hearing the voices I don't blame people for not wanting them into their cities. 1 is high (or addicted) to skooma (addicts are known to steal to get their next fix). If you finish the thieves guild special quests you soon realize why they're outcast in big cities. They are indeed smugglers and thieves.