Answer:
I reach for the sky, but clutch to the ground. Sometimes I leave, but I am always around. What am I?
I run around the city but I never move.
Six letters do my name compound; among the aged oft I'm found; The shepherd also by the brook hears me when Leaning on his crook; but in the middle me divide and take the half on either side each backward read a liquor tell ev'ry gay toper knows it well.
As a stone inside a tree, I’ll help your words outlive thee. But if you push me as I stand, the more I move the less I am.
I have a few points but we're not competing. I'll help you win when you're eating.
Some try to hide some try to cheat. But time will show we always will meet. Try as you might to guess my name. I promise you'll know when you I do claim.