Well, why not?
I think my first visit was driven by curiosity: I'd seen the Confiteria Ideal in film, I loved the music and the dance, and I just wondered how a visit would work out. I'd also watched Tete and Sylvia on YouTube, and since they never came to London and it seemed impossible to find their travel plans, I hoped it would be possible to meet them there and take classes. (It was.) I rented a flat, so I knew that if the tango didn't work out I could just sit and read for a few weeks. I expected it would be excruciatingly embarrassing at times, and very rewarding at others, and it was. I imagined I'd dance all night every night: it never occurred to me to wonder, before I arrived, with whom? I found it a difficult, vast city (a lot bigger than London), functional but somewhat run down on the surface, with a lot of joy and misery in it, and with many extraordinary buildings. And everywhere I went, incredibly welcoming people, and not just in the tango community. I guess tourism is a new phenomenon there: during the lifetime of almost everyone you meet no one, or very few tourists, ever visited Argentina. Meeting visitors may be an affirmation that the country is a normal part of the world, and no longer isolated. Anyway, it's a remarkably hospitable place.
As for tango, I think the experience is different for visiting guys and girls; strange! In any case, every individual's experience is going to be different. With one exception my experience was of the milongas in my vicinity, which are well-known and where there are usually a few visitors. My impression is that a visiting guy has to be an excellent leader to get much dancing in that gentle, undemonstrative, highly musical dance of the downtown milongas. Whereas if his partner can follow a lead comfortably, she's likely to find she'll be kept quite busy. 'Milongueros' are humans, and curious about visiting women who look as if they dance well. I think the women are curious about visiting guys, too, but their situation is different, and understandably they are less eager to put themselves in the arms of someone they don't know and haven't danced with before, on a crowded floor. Or else, they can find better partners than me.
I first went to explore, and it was useful, so a return visit seemed inevitable. I had contacts, I knew my way round a bit, I felt I could build on the first visit. & I got what I needed: some very experienced eyes on my way of walking, of stepping, of standing. Argentine teachers in London seem eager to thrust amazing, inventive steps at you, but the teachers I looked for were more likely to watch quietly, and their brief comments were very helpful and illuminating. Or, like Pedro Sanchez, they'd go over something absolutely basic again and again if they weren't satisfied: they know from very long experience how it ought to look. Exactly what I wanted and needed, and something not so easy to come by in London. More than that, when someone like Alberto Dassieu encourages you, you really feel you have a contact you have to live up to. & there's an enjoyment of tango that gives it value. Does tango matter that much to me? Like most of us, I guess, yes and no. I love it, it's given me a lot, but it's not part of my life to the extent that it is for Pedro or Alberto, and I can enjoy other lives too. However, it's usually true that the more you put into something the more you get out of it. & the music sounds better there: a truly proud, strong music. I don't know why it just doesn't quite ring out like that in London. Nothing to do with the volume.
So do I want to go back? I guess the answer's obvious. There are teachers there who told me 'Remember, you have friends here!' My first real encouragement in tango was Ricardo Vidort whose wholehearted, good-natured enthusiasm for that close embrace and musical dance, encouraged me: sadly he's no longer around, but his lifelong friend Osvaldo Cartery still is, and I've yet to meet him. & I was introduced to Muma, who gave me her card at a milonga one evening and said to call her, and I just didn't have time. & I've never been to Lo de Celia, or Gricel or... There's much to go back for. Only... I was welcomed so warmly that I'd be ashamed to go back and still not be able to talk much, so I'm having to work on that. Lenguajero might prove very useful.
So my conclusion, for what it's worth, is that for a guy who likes the older tradition it's worth visiting for the teaching, and for a girl it's worth visiting for the dancing. Of course I'd be interested in other views on that. This posting was prompted by Ms Hedgehog, and by Tangocherie's reply.
Incidentally, those tango-enthusiast taxi drivers everyone talks about. Why did they never pick me up? Well, once or twice. Mostly I got Cumbia and Latin rock. Which was what I heard on the streets too. & I was told that while very few people have an active interest in tango, the tango songs are a part of everyone's cultural heritage. Those complex, beautiful poems are widely remembered, just as we all remember songs like... 'She loves you, yeah, yeah yeah'.
Ah, the buildings... Palacio Barolo has to be the ultimate. It was designed in the early 1920s by an Italian-born architect obsessed with the Divine Comedy, and the entire building is designed as a model of Dante's triple world. 100 metres high, and crowned with a lighthouse (God). I still haven't visited it, so there's definitely something to go back for!
Video thanks to Malenatango.