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Oh, good, you're here. Now, there's a bit of a problem; hopefully you can help with it. Lily -- she's my friend, and she's a little... uh... how shall I say this? You know the professor you might have had who was constantly forgetting things, because she was so absorbed in her own mind? Lily's kind of like that. One might call her "many-layered". Only she usually only functions on the deeper layers. Kicking her back to reality can be a difficult task sometimes.

Anyway, back to the problem at hand. Twenty days ago, she left on a trip. Taking off like this is fairly common. Heck, she's probably been out of the country more than she's been in it the past couple of years. Except this time she's been gone a lot longer than usual.

Can you help me? After she'd been gone a week (she usually never stays away more than five days), everyone began to worry. Plus, usually, she leaves an itinerary with all of her friends so they know where she'll be. I'm really starting to worry.

The only thing she left behind this time was the list of cities below. And it's weird, because her blog indicates that she hasn't been to the first three cities on the list, but she's been to some of the others further down, so this can't be an itinerary.

Lily needs your help! Something must be encoded in the list below; please figure it out and determine where she's gone, so we can get her home safely!

Kigali
Muscat
Juba
Malabo
Luanda
Kampala
Bata
Pago Pago
Antananarivo
Chișinău
Yerevan
Windhoek
Lagos
Bucharest
Muscat
Skopje
Asmara
Schaan
Santo Domingo
Tegucigalpa
Baku
Nairobi
Andorra la Vella
Quezon City
Nouakchott
Tashkent
Mbabane
N'Djamena
Tirana
Nuku'alofa
Zurich
Astana
Reykjavik
Díli
Caracas
Dubai
Vientiane
Muscat
Valletta
Addis Ababa
Istanbul
Kingston
Algiers
Bishkek
Saint John's
Moscow
Dodoma
Buenos Aires
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We can get a hint by

reading the first letter of each sentence to get ONLY LOOK AT THE CAPITALS

Using the above on the list of cities results in:

Kigali, Muscat, Juba, Malabo, Luanda, Kampala, Pago Pago, Atananarivo, Chișinău, Yerevan, Windhoek, Bucharest, Muscat, Skopje, Asmara, Santo Domingo, Tegucigalpa, Baku, Nairobi, Andorra la Vella, Nouakchott, Tashkent, Mbabane, N'Djamena, Tirana, Nuku'alofa, Astana, Reykjavik, Díli, Caracas, Vientiane, Muscat, Valletta, Addis Ababa, Kingston, Algiers, Bishkek, Saint John's, Moscow, Dodoma, Buenos Aires

moving on:

Seeing as Muscat appears multiple times and it's country (Oman) is the only country in the world that begins with an O, we can deduce that the first letter of the countries associated with the capital must be of significance. Using the first characters associated with the countries of these capitals (from Beastly Gerbil's answer) gives us the string ROSEAUAMMANROMEDHAKAMUSCATKIEVLOMEJAKARTA

almost there:

it's pretty clear that this string is once again a list of capitals: Roseau/Dominica, Amman/Jordan, Rome/Italy, Dhaka/Bangladesh, Muscat/Oman, Kiev/Ukraine, Lome/Togo, Jakarta/Indonesia

and finally:

if we once again take the first character of the countries we get DJIBOUTI, the location of the missing friend!

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Work in progress:

Some more data about the cities:

Kigali              Rwanda
Muscat              Oman
Juba                (South?) Sudan
Malabo              Equatorial Guinea
Luanda              Angola
Kampala             Uganda
Bata                Equatorial Guinea
Pago Pago           American Samoa
Atananarivo         Madagascar
Chișinău            Moldova
Yerevan             Armenia
Windhoek            Namibia
Lagos               Nigeria
Bucharest           Romania
Muscat              Oman
Skopje              Macedonia
Asmara              Eritrea
Schaan              Liechtenstein
Santo Domingo       Dominican Republic
Tegucigalpa         Honduras
Baku                Azerbaijan
Nairobi             Kenya
Andorra la Vella    Andorra
Quezon City         Philippines
Nouakchott          Mauritania
Tashkent            Uzbekistan
Mbabane             Swaziland
N'Djamena           Chad
Tirana              Albania
Nuku'alofa          Tonga
Zurich              Switzerland
Astana              Kazakhstan
Reykjavik           Iceland
Díli                East Timor
Caracas             Venezuela
Dubai               United Arab Emirates
Vientiane           Laos
Muscat              Oman
Valletta            Malta
Addis Ababa         Ethiopia
Istanbul            Turkey
Kingston            Jamaica
Algiers             Algeria
Bishkek             Kyrgyzstan
Saint John's        Antigua and Barbuda
Moscow              Russia
Dodoma              Tanzania
Buenos Aires        Argentina

We observe:

All cities mentioned are the most populous in their country, with the exception of Malabo, which is the capital (Bata is the most populous city of Equatorial Guinea). Of course, in many cases capital and most populous city are the same; the exceptions: Malabo/Bata, Lagos, Schaan, Quezon City, Zürich, Dubai, Istanbul.

If this puzzle would simply be 'find the one that doesn't fit', it would have to be

Malabo, for the above reason.

However,

Muscat appears thrice, suggesting that there is more to this puzzle than find-the-one-that-doesn't-fit. Note that Oman, where Muscat is located, is the only country that starts with an O - so it might be that some message is hidden in (the first letter of) the country name.

Combining the country names,

more specifically, the first letters, we get: ROSEAUEAMMANNROMELDHAKAPMUSCATSKIEVULOMETJAKARTA

We can also read that as:

- Roseau (Dominica)
- Amman (Jordan)
- Rome (Italy)
- Dhaka (Bangladesh)
- Muscat (Oman)
- Kiev (Ukraine)
- Lome (Togo)
- Jakarta (Indonesia)
Every two cities are separated by one letter: E, N, L, P, S, U, T. Interestingly, these letters are from the cities that are not capitals. The letters of the new countries form DJIBOUTI.

I am not sure yet how to combine these two last results.

Is the trick that we only have to use the capitals, and can ignore E, N, L, P, S, U, T? Or is there some system behind those letters as well? The real capitals for those records are Malabo, Abuja, Vaduz, Manilla, Bern, Abu Dhabi and Ankara, but concatenating their first letters doesn't yield something useful: MAVMBAA.

Perhaps the following:

The question mentioned that Lily hadn't been to the first few cities, but had been to a few others further down. Then, perhaps the system is that those cities not used to form Roseau, Amman, etc. are the actual itinerary: Bata, Lagos, Schaan, Quezon City, Zürich, Dubai, Istanbul. The final destination is encoded, i.e. Djibouti. The problem with this theory is that it assumes that Lily did not want to visit any capital city except her final destination. But it's the only way I see at the moment to make sense of the not-capital cities.

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Not an answer, but I've been told this will help.

Below is a list of the countries each city belongs to:

Kigali - Rwanda
Muscat - Oman
Juba - Sudan
Malabo - Guinea
Luanda - Angola
Kampala - Uganda 
Bata - Guinea
Pago Pago - Samoa
Atananarivo - Madagascar
Chișinău - Moldova
Yerevan - Armenia
Windhoek - Namibia
Lagos - Nigeria
Bucharest - Romania
Muscat - Oman
Skopje - Macedonia
Asmara - Eritrea
Schaan - Lichtenstein
Santo Domingo - Dominican Republic
Tegucigalpa - Honduras
Baku - Azerbaijan
Nairobi - Kenya
Andorra la Vella - Andorra
Quezon City - Philippines
Nouakchott - Mauritania
Tashkent - Uzbekistan
Mbabane - Swaziland
N'Djamena - Chad
Tirana - Albania
Nuku'alofa - Tonga
Zurich - Switzerland
Astana - Kazakhstan
Reykjavik - Iceland
Díli - Timor-Leste
Caracas - Venezuela
Dubai - United Arab Emirates
Vientiane - Laos
Muscat - Oman
Valletta - Malta
Addis Ababa - Ethiopia 
Istanbul - Turkey
Kingston - Jamaica
Algiers - Algeria
Bishkek - Kyrgyzstan
Saint John's - Canada
Moscow - Russia
Dodoma - Tanzania
Buenos Aires - Argentina 
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