You can go to Machu Picchu without having to do any climbing. Also it's not that high to normally feel the thin air (2400 meters altitude). You only have to do hiking if you also want to visit the viewpoint on the mountain (but that's optional).
I usually don't like such hot-spots with so many tourists, but I'm glad I was there! I went there by my own without a guided group and found some quiet spots there.
I'm really into mountaineering and hiking - but what's on my anti-list: climbing Mount Everest. I wouldn't do it for free - for me this has nothing to do with a nature experience: