One wonderful aspect of the week-long math conference in Europe, in particular, is that while Monday, Tuesday, Thursday, and Friday are entire days of lectures, Wednesday often includes the afternoon hike. Germans especially seem to love the hike, and they have convinced me! The afternoon hike gets the whole group out of chairs and into nature. The group rambles along at a relaxed pace (except for the overachievers at the front) chatting about math, not-math, and everything in between.
It's important to give the brain a little break so that it can do its unconscious work of solidifying connections and giving rise to new ideas.
A walk in the woods has also been shown to increase the capacity to focus. It's as effective as drug therapy for some children with ADD/ADHD.
You get to meet people you may not have talked to otherwise as the group stratifies by walking speed and style.
You get to see the place you're visiting in a new way, as well. I went to Boston for the Joint Math Meetings last January. Boston for the first time... and I saw essentially none of it, for there was no conference ramble. Between interviews and talks and panel discussions I never made it farther away from the hotel than the wonderful Indian restaurants two blocks away one direction and the Charles river. I saw MIT from a distance...
By contrast, on a visit to Oberwolfach I got to meet a goat!