I used Wikipedia to look at the 50 most populous world capitals, and then saw whether or not TAR:US had visited. Of the top 50, TAR has visited most. Here are the rest:
Improbable - (capitals of) Iran, Colombia, Iraq, Syria, Saudi Arabia, D.R. of the Congo, North Korea, Afghanistan, Jordan, Cuba, Venezuela, Sudan
Possible (population ranking in parenthesis) -
Jakarta, Indonesia (5) - only a previous airport visit
Ankara, Turkey (17)
Madrid, Spain (24)
Nairobi, Kenya (31) - only a previous airport visit
Brasilia, Brazil (32)
Luanda, Angola (35)
Pretoria, South Africa (36)
Tashkent, Uzbekistan (38)
Rabat, Morocco (45)
Minsk, Belarus (50)
Now, there's nothing special about going to the capital of these countries. Indeed, TAR:US has visited Turkey, Spain, Brazil, South Africa, and Morocco, so perhaps a visit to the capital would be superfluous. (I disagree, especially with Spain...but I'm biased, being a Spanish teacher.) And some of you may think some of my 'possibles' should be 'improbables' (Angola, Uzbekistan, Belarus, among others perhaps). But this list isn't meant to be anything definitive...simply informative with slight biases from my opinion. Also, note that my cut-off at 50 was merely arbitrary. i.e. I got tired of doing the list.
Anyway, perhaps you'll find it interesting.