Maybe this makes me an "ugly American" - if so, so be it. But in my experience, I find that using the "politeness words" in a language that I otherwise don't speak at all just creates a lot of unnecessary awkwardness.
If I greet someone in the local language, they'll generally assume, not unreasonably, that I'm prepared to converse in that language. When it comes to light, five seconds later, that I'm not, there's then the question of what language they should use instead. (They may know that they speak perfect English, but they don't automatically know that I speak English.) But if I greet them from the start with "hello," that tells them straight away that I'm an English speaker, and it's just easier all around. (Notably, my travels so far have taken me mostly to places where most people do speak some English. If I were going someplace where that wasn't the case, I'd take a different approach.)
In languages like German and Italian, where I can make myself understood well enough to complete simple transactions, but not hold complicated conversations, I find that the most useful "politeness phrase" is "I'm sorry, my (language) isn't very good." That often works better than "Do you speak English?", because it gives the (store clerk, waiter, train conductor, random person approaching me on the street) the option of switching to English, speaking more slowly and simply, or just leaving me alone if what they had to say wasn't very important. I've gotten all three responses in approximately equal numbers.
But in languages like Slovene, Danish, or Icelandic, that I'm not reasonably going to become proficient enough in to handle even simple exchanges, I'd rather just establish as expediently as possible that I need to converse in English.