I can certainly tell I'm not as young as I used to be, but I don't feel at all different from 20 or even 30 years ago.
I'm 71.  I'm the healthiest person I know at my age.  I don't take any medications.  I have almost no limitations on what I can do, compared to a decade or two ago.
It's possible that not having grandchildren (I have one grown son who is highly unlikely to give me grandchildren) makes a difference.  It's hard to be sure.  Because I have friends and a sister with grandchildren, and through them realize the genuine joy involved; nonetheless I think that no grandchildren has helped keep me young.  I will hasten to point out that I was 34 years old when I had my first child.  Not terribly old, but certainly not young.  And as I went through the years of being a parent (mom, in case that matters) I came to think that being a slightly older parent did keep me somewhat young.
But back to your question.  I relocated from Overland Park KS to Santa Fe NM 11 years ago, right before I turned 60.  I made the move because of a divorce.  The relocation was the best possible thing for me.  I can say that Santa Fe is a wonderful place for an older woman to re-invent herself.  I have no idea what it's like for a man, but I hope it would be as good.  I will say that I wouldn't want to be a young person here, as they roll up the sidewalks at 9pm.  I had the good fortune to have my dissipated youth in the Washington DC area.  After the Pill, and before AIDS, if that matters.
My personal story aside, I think that what truly matters the most is your personal health.  If you are very healthy, there won't be a lot of difference between you 60s and your 70s.  If you're experiencing health problems, there will be a difference.  But no matter what, your personal attitude matters.  If you're confident and optimistic, you'll do well.  If you're defeatist and pessimistic, not so well.