A very nice question -- I certainly know the experience you describe, that feeling of intense aliveness. As a first remark --  almost like a kind of lucid dreaming, where one is suddenly thrust into a completely alien environment in all of its precision and intricacy. Or rather, a kind of experience with all the latent possibility of dreams, but without the feeling that this comes from your own imagination: the exhilaration of encountering something which is really other, really outside yourself. It reminds me of the discussion on encountering beauty: post 

I think the feeling of exhilaration Dave and Mia were describing - which I can certainly relate to - is not caused by an experience of foreignness, but rather by a balanced combination of foreignness and familiarity. For example, I believe most Europeans who go to huge cities such as Beijing, Lagos or Mumbai will not be exhilarated, they will be shocked. They might be fascinated by the foreign, but they will find it hard to experience anything deeper than fascination, because that requires some level of communication, of understanding what's going on around you.
On the other hand, if they go to another European city or to an American one, everything will be familiar enough to allow contact, yet different enough to fascinate, and this ability to be inside and outside is, I think, the essence of the exhilaration one feels in a foreign city.
I think of Marguerite Yourcenar's Emperor Hadrian, who travels the Roman Empire and enjoys the uniformity which exists in the very heart of the exotic: from Africa to the Black Sea, in the most diverse cultures, every city in the Empire has its forum, its market place, its gymnasium, its uniform grid of streets. So even if you don't speak the language and you've never been there before, you know your way around, you're not completely lost. You're a foreigner, but you're also at home. This is of course all the more true in our own global culture.

Just to respond to "combination of foreignness and familiarity" -- there is a very interesting effect which comes from visiting a place which you know intimately from literature (perhaps also from cinema, though here the effect is different). For instance, having grown up on the glories of English literature, it was strange for me to finally visit England and experience myself, for a time at least, as a foreigner there. An American friend made a similar remark, though as I recall her disillusion (that is her feeling of perhaps being an outsider, as well as an insider, in English literature) came from an offhand remark of Woolf's that Americans do not know whether or not to laugh when they read Chaucer, but hesitate at the crucial moments...

In any case, one thing that cities offer us over small towns is a certain openness to narrative -- one is part of such a mad rush of stories and somehow, in any case, so much in the midst of images and words that the power of retelling one's life, reorienting oneself, dreaming differently, is somehow closer to the surface. In small towns, one is so caught up in the particularities of type and character which one sees that it is easy to become simply a casual observer -- there is less of the compulsive need to process the overwhelming sensory data of a city by stepping back, telling a story, and actively putting things -- and so also oneself -- into language.