If you talk to Lucas Simms and ask him about the area outside of Megaton you'll get a map marker for Rivet City. The weapons vendor there always has a lot of ammo in stock.
(If you haven't done much of the main quest it might be a good idea to avoid talking to the people in the science lab in Rivet City. I won't spoil it for you with the how or why.)
You also get a mapmarker for Tenpenny tower in the bar in Megaton I think. The vendors there also have plenty of ammo.
There are more vendors, but these two are probably the easiest to get to in the beginning. Unless you want to wait outside of Megaton for Lucky to show up.
There's also a Brotherhood Outcast fort southwest of Megaton, where you can turn in certain items for 5.56 ammo.
The 5mm ammo is for the minigun, which you will mostly find on supermutants. The minigun will go through 250 rounds in no time, so if you ever want to give it a go you'd best save up some more.