I need to say that being in a new city is always challenging. And more if you're on your own (alone). I went to Hawai'i last month, to Honolulu. And found it cautivating myself with its mood. What I mean is that, there were a lot of people looking for the same: a new experience, just look, know people, most of this people are not looking for commercial tourism, just some experience.
There are a lot of foreigners. The day I arrived I found the streets full of Japanese people, just before the Honolulu Marathon. I watched them, not all of them be be unfair, but in the commercial mood, you know? On the other hand there are people living there, because they move from crowded cities, or another rhythm of live. May be surfers, or just travelers.
I found it interesting, because Cusco is about the same, in terms of people moving there, working or running business, just because the city is magic, and you can find people from everywhere. As in Honolulu, in the commercial mood, or just the mystical mood. I went there in both so I can explain how it feels!.
Both are not big cities, one is right in front of the sea (or in the middle of nowehere in the Pacific Ocean) the other, in the middle of the mountains. In both, you can feel the mood of the native people, or the people that just move there lo enjoy living on sush a place like this.
By the way, take the "Cosmopolitan" definition in the way you want. For me it is just to have different cultures, and moods in the same place.