If there is one thing that I can say I do right, and even advise to others, it is the fact that I make it a point to see my grandparents (both sides) at least once a month. And call them every couple weeks.
More than the connection to your family's history, a continued conversation with your grandparents will help you to understand the world and provide a phenominal sounding board (grandparents never lie, they are too old to worry about hurting feelings). Plus they exude pure love, no petty jealousy, no outside influences, only pure love driven simply by your presence.

This weeks homework assignment is to call or visit your grandparents.

side note: my brother chris hand writes letters to my grandparents. You know what I heard about all lunch yesterday? Chris and his stinking letter. You made their day Chris. It was awesome...