Do you have a set routine for what you do, immediately after leaving the vault? Me, I always head straight for Megaton first. If I have something to sell, I sell it. I help out the water pipe guy for xp and the ability to sell Scrap Metal to him. I then disarm the bomb so that I can get a place to live. After that, I talk with Moira and at the very least do the first part of her questline, going to Super Duper Mart. That's a great way for me to get valuable loot early in the game (weapons, ammo and stimpaks) to stock up on and sell. And xp, of course. I often also do the rad quest for her, as it's very simple.
After all of that, it varies. Usually I will just head vaguely for Rivet City, exploring the ruins I come across on my way.