Conan: (reading the letter in the chest) The treasures you seek are the memories of the adventures you had figuring out the map. You crossed rugged terrains, and no doubt overcame many dangerous obstacles along the way. And you did this together. That's why you should treasure this day. You may not understand this now, but some day you will, so don't forget what happened today, or the people standing right next to you. These are the things to be remembered. And I hope you've collected a few stories you will be able to pass on to your kids.
Conan's reaction when Dr. Agasa tells him the whole story about the map led me to believe his parents were dead. It is revealed later in Conan is Kidnapped that they are travelling the world.