First off – Mazel tov on the birth of what I am assuming is your first grandchild. You should have a lot of nachas from this child and all of the future ones, byz”H.
Not coming from a religious background and hardly knowing my grandparents, except for my mother’s mother and my father’s father (and him only briefly), I have always envisioned grandparents as being in a backup support role for their children. With the parent’s permission, I would suggest having a treat ready for boys who memorize mishnayos or other good deeds. I remember my father, who was almost 80 at the time, trying to teach my 6 month old son how to crawl. Memorable pictures from that.
Most of all, I would say spend time with your grandchildren. Tell them about yourself, about your parents and what you know about your grandparents. Make sure they know their family heritage. Give them Jewish pride. Love them!