The best way to get local weather is to get a Weather-All Hazzrds Radio .. SAME technology optional. You want one that has an EXTERNAL ANT jack so you can put a Scanner, or 2-meter ham, antenna on the OUTSIDE (roof is nice) of your RV (NOTE Pay attention to overhall height, Hitting bridges can damage the antenna).
NO need for Internet or Television reception.. Most of the US is covered by one of the NOAA transmitters. plug they can wake you up if the need is broadcast (IE: Tornado watch/warning).