The U.S. Airport/Facility Directory consistently lists 1-800-WX-BRIEF as the phone number for any Flight Service Station (FSS). Unfortunately, the toll-free numbers don’t work for a Canadian cell phone, even when you’re in the U.S. — that makes life hard when you want to close a flight plan after landing at a non-towered airport (for example), or get a weather briefing while you’re in the taxi on the way to the airport.
Fortunately, I’ve just found this PDF list of local numbers for all U.S. FSS. Once I actually had to call Nav Canada’s toll-free FIC number just to have them look up a U.S. FSS number for me — I’m printing this out and putting it in my flight bag so that that doesn’t happen again. They’re also useful for getting a U.S. briefing from a Canadian landline.