Exercise is my particular interest in this topic. I'm in direct contact with people involved in this research, one of whom lamented to me "exercise isn't patentable." I've read a couple times in the literature that if the benefits of exercise could be provided in a pill it would be by far the most prescribed pill ever. Our medicated society is in reality compensating for being a sedentary society.
On the basis of what I've researched if I had to pick one exercise activity that is the best it would be high energy dancing. This combines cardiovascular, foot falls, balance and social benefits. For example, contra dancing 4-5 times a week should really keep your brain humming. Unfortunately, this is not practical for many, at least not at that frequency. It's not practical for me.
What I think might be the second best would be trail running. This combines cardiovascular, foot falls, balance (negotiating trail obstacles) and meditative benefits. Activities that involve the foot striking the ground increase blood flow. Running, hiking and dancing are superior to biking, swimming or skiing in this regards. The drawback is that foot fall activities increase the chance of joint pain, though a wise approach and plenty of antioxidants in your diet can mitigate this.