I live in a Maryland suburb of Washington, D.C., and the weatherman thought we'd be able to see a rocket launched from Wallops Island (alas, it blew up instead) which by car is 166 miles away. Assuming that I have a clear view of the horizon (I don't really, but perhaps I could go to a nearby 19-story apartment building), and clear skies, how far from the launch pad would the launch be visible to the naked eye?
Here's a map that shows the general visibility for Antares launches (that was the rocket the weatherman was talking about, although it won't be flying again until 2016):
I once watched a Minotaur V launch from Wallops down on Brighton Beach in New York. It was clearly visible. It was also a night launch, it probably wouldn't have been visible during daytime. Minotaur V is less powerful than Antares, so if you had a clear view of the horizon, you should definitely be able to see an Antares launch from DC.
Also, it's not a NASA rocket. The Antares (and the Minotaur V) is built by Orbital Sciences Corporation. Currently all manifested missions of the Antares are under contract with NASA.
I was able to easily see a night launch from Wallops a couple years ago from an apartment building in Baltimore. It took about 45 seconds from launch to be visible, but it was plenty bright (even with the light pollution of a large city) to see it. It was headed pretty much straight away from my location so it didn't show much movement, but it was clear to see the MECO event and then the 2nd stage light off. After that point it rapidly got too faint to see.
It did help to also have a live webcast to know when to watch for it, though I noted that the "live" webcast was about 20 seconds delayed from what I saw seeing with my eyes.