6250 is actually the robotic-sounding weather broadcast of the "United States Coast Guard Master Station Atlantic", not the NWS. I occasionally can copy it out here in the NW during the summer-early Winter months. (In fact, it's been coming in like a blowtorch here lately.) I think they only transmit once every couple of hours or so.
If I remember right, the equally robotic-sounding USCG Master Station Pacific in Honolulu transmits on the same frequency during the other parts of the day.
There are other freqs as well, but I don't have my list with me right now.