Cristo Redentor

You go, and you should, and then you spend most of it looking at the back of other people's phones. Get there as early as you can manage - by mid-morning the platform is shoulder to shoulder and everybody is lying on the floor trying to fit the whole thing in one frame. The statue itself is worth it from directly underneath, which is the angle nobody puts on a postcard: enormous, plain concrete up close, and much more impressive for it. Give it half a day by the time you have queued at both ends.