Most of the airports I have flown from in the USA have FBOs who have internet equipped planning rooms which can be used free of charge. Having said that these have been mostly municipal airports.
1-800-WX-BRIEF is not just for the weather, but also NOTAMS, flight plans, ATC info etc. Pilots are encouraged to call before every flight and every flight leg.
I believe that the people at 1-800-WX-BRIEF use
http://www.aviationweather.gov, but I could be wrong.
NOTAMS can be got here
https://pilotweb.nas.faa.gov/distribution/atcscc.html and here
http://www.faa.gov/NTAP/