Megaton
Once outside, let's take a look around. A vast wasteland opens up before us, one we could spend hours exploring. But the main quest is top of mind. So, open the Pit-Boy, turn on the radio, and head to the first town – Megaton. To do this, head down the hill toward the ruined houses and turn right. Climbing the hill, we come to a town surrounded by a large fence. Near the entrance, there's a beggar you can share clean water with and boost your karma with.
We enter the town and immediately run into the sheriff, who's eager to tell us he's the law here and all that. We ask him about the town and tell him we're looking for our father. He recommends going to Moriarty's Saloon. We head there. Getting information out of the old man won't be easy; several options are provided below.
How to find out where my father went
1. You can pay a hundred caps and learn everything you need. However, you might have problems with the local currency at the beginning of the game, so this option won't suit everyone.
2. Convincing the innkeeper to give up information for a pretty face will be extremely difficult, but it's worth a try. It all depends on charisma.
3. Stealing will help out in difficult situations. We hack Moriarty's office, then do the same with the computer, where we find all the information we need and even more.
4. We accept a small task from Moriarty: find a prodigal woman who has escaped from him and owes 100 caps, and kill her. Open the Pip-Boy and go to the indicated location. We enter the house where the victim is hiding. We talk to her and learn that Moriarty is no angel either, although this is immediately obvious. Next, we choose what to do. You can kill her, take the caps, and pay Moriarty back (minus karma). But we are kind people, and we will not touch fallen women.
So we either just let her go and tell her we'll trick Moriarty (then we'll still have to pay him 100 caps out of our own pocket), or we demand 300 caps (or 400 with persuasion) for our silence, after which we give the innkeeper a hundred and keep the rest.
Ultimately, regardless of the path we choose, we learn that Father was in town (the sheriff told us this at the entrance), and more than once. It turns out we weren't born in Vault 101, and all the stories we've been fed throughout our lives are complete nonsense. But most importantly, we know where Father is headed. The Galaxy News radio station is the next destination.
Source: SSoHPKC
See also:
Fallout 3: Rivet City
Fallout 3: Vault 112
Fallout 3: M. Jefferson