A trend in Israel today among the orthodox Jews is the creation of Avot Uvanim(fathers and sons) study groups. There are over 800(!) such study groups in Israel. My 8 year old son and I joined one of these groups a few months ago and we really love it. Once a week all the members of the local Avot Uvanim branch meet for an hour of learning in a neighborhood synagogue. It is a truly beautiful sight to see all the fathers and sons sitting together and learning, fulfilling the mitzvah of "veshinantam levanecha"(and you shall teach them diligently to your sons(Deuteronomy 6)). The racket created by the father-son chavrutot produces a festive atmosphere. At the end of the learning session, the children receive a prize: usually some kind of sweet. The fathers also receive prize: The joy of spending quality time with their sons in this world and the reward of learning/teaching Torah in the next world.
If you are interested in joining or starting a branch you can call 1-700-500-613 in Israel or 212-5615877 in the United States.