I can't recall ever getting a radiant quest from anyone in Solitude, In other holds they are gotten from the Jarl or his Steward or from inn keepers. Am I missing something?

In addition, I don't get any that involve the foresworn in Markarth. It seems that I had with an earlier character.

Any thoughts?

Do you not talk with the NPCs from Solitude? Almost half of them give you misc quests.

If you mean ones you can repeat, then no. None that I can think of.

The Jarl of Markarth is supposed to give you a couple of Forsworn ones. So does the nice, totally normal pawn shop lady.

Tons of people in Solitude have minor quests, but I don't think there are repeatable ones. Try asking Falk Firebeard. He may have some. I can't remember.

You mean bounty jobs? Leave the city for a while and try again. See if you have other radiant quests (not bounty jobs, more like "fetch this-and-that in Random Dungeon) active and finish them first. I recall having that problem in Windhelm once, but it solved itself later.