I think you're best just using the METAR data from the real world, after all that's what the PCs would be using. It's easily available via the web (I use skyvector.com to find stations) and if they move a long way quickly you can get the data from the new location much more quickly from a laptop or tablet than you could generate realistic weather with dice. If they go away from a convenient METAR station then just find one in a reasonable similar situation.
The big blind spot is the open sea. Depending on where you are in the world you might be able to find shipping forcasts that cover the area.
Historical METAR data is available too, so you could pick a year and use the data from that to represent the in-game weather.