Tecnically, Vatican City is part of Rome, so maybe it should be included. Then Monaco is inhabited since ancient times and Budapest had been founded as Aquincum by the Romans
Delhi is ancient, but the capital New Delhi wasn't founded until 1911, when "George V and his consort, Queen Mary, laid the foundation stone of New Delhi at Kingsway Camp." What do y'all think?
OK, I added San Marino, which was founded in 301. But the area of Rome which is the Vatican doesn't appear to be settled until around 848. Of course, let me know if that's wrong.
Amman, Jordan is very ancient - the oldest version was pre-7000 BC and it was a well established city in classical antiquity (it was called Philadelphia)
It's an interesting case because it fizzled out and the modern Amman was founded as a caravan stop on the route to Mecca in the 1800s (if I'm not mistaken).