As you've escaped from the Vault, you now need to find your father - it's the only lead you have to what's going on.
As you noticed from the overseer's terminal, there is a settlement nearby called Megaton. When you enter the city, you are welcomed by the sherrif, Lucas Simms - although he doesn't recognize seeing your father going through, he does recommend asking around.
Your first lead is in the Moriarty Tavern - you can obtain information about the father by talking to Moriarty who will give out the information for about 100 caps (or quick talkers). If you don't have enough caps, he recommends that you can deal with a druggist within Springvale to obtain these caps, since she stole money when she stopped working for him.
Once you get the Dad's current location, you can then head to Galaxy News Radio in order to talk to Three Dog - the DJ from the radio. At this point, you may want to look into sidequests available in order to prepare for the DC ruins. It is recommended to be at least level 5 before trekking to the Radio station.
When you reach Galaxy News Radio, you'll notice that it's under siege by Super Mutants as stated by the Paladin from the Brotherhood of Steel. You can either kill the mutants yourself, or let the soldiers help you.
Before you can enter the building, a Super Mutant Behomoth attacks. This opponent is very powerful and fast and can quite easily kill unprepared players; however, you can retrieve the Fat Man from one of the fallen initiate to use against the Behmoth - it should take about three hits to take him out.
Note: You can proceed directly to vault 112 for completing Tranquility Lane. If you choose to do that, the game will treat the intermediate quests (aside from Galaxy News Radio as completed. In addition, if you later want to assist Three Dog with his station, you will have to fight the Super Mutant Behemoth without assistance from the Brotherhood of Steel and their fat man (unless you purchase it from Rivet City.)