Hm. The most exotic, faraway place I've ever gone for research is the local tavern. :) But even from that I can say one thing: it depends. Mostly on whether the locations are just for color, or are going to have an impact on the plot. If there's a chance that you'll learn things that affect the plot, and you don't want to have to ditch large chunks of draft and rewrite, go earlier. If you're just after colorful details, you can go later. Which may mean that the less familiar the place is, the earlier you should go, since you may not know whether the things you'll learn will affect the plot.

Thus I think the answer is that it varies, not only from author to author, but from story to story. Do as much preliminary research as you can, and that will give you a better idea of not only when is the best time to go, but what you need to pay attention to once you get there.