This has a lot more to do with money than it does with age, especially in cities where there are neighborhoods in the center or near the center.
As for a yard, some of the richest billionaires in Manhattan don't have one. It's a matter of preference in which age isn't really a factor. Do you want a yard, or do you want floor-to-ceilng windows with a cityscape view? That's the choice in a select few cities like Manhattan, but in the majority of cities you definitely can get a yard very close to the center if that's what you value; it's just a matter of how wealthy you are.
Here in Houston, personally I don't know a single person who would prefer to live in Sugar Land (a suburb about 30 minutes out) over River Oaks (a very affluent neighborhood of gated mansions in the geographic center). But only the top executives, neurosurgeons, sports stars, etc., live in River Oaks because everyone else is priced out.
Some people value a yard and brick house so much that they commute in order to get it. Others buy high-rise condos and enjoy the panoramic views and central proximity. I haven't really observed much true correlation with age, though, with the high-rise condos. Apartments, yes, but expensive condos, no.