Mike-Bracknell,
It depends on the type of flight.
If you're talking about ain airline flight, the distances travelled mean that the aircraft will transit so many weather systems that I can't suggest where to look.
If you're interested in a light aircraft flight (some kind of trial lesson, given the non-pilot audience) then my experience from several years wrestling with weather forecasting for gliding suggest the following:
1. The forecast the day before is usually pretty close - good enough to tell if (a) it's flyable and (b) roughly what kind of weather can be expected. All you can get from forecasts further ahead is a trend, unless you know what you're looking for.
2. For a non-pilot I'd recommend the Met Office site -
Met Office: UK: forecast weather (click on the region where you intend to fly). This gives some idea whether it is likely to rain (solid rain = bad, but if showers you can fly in between, unless thunderstorms are forecast in which case it might be foolish to fly), how windy it will be (anything over 15-20 mph you might ring the airfield on the day to check whether it's too windy - wind direction is important, but a non-pilot won't know enough to know the difficult directions). This will give a general idea whether it's likely to be a pleasant flying day.
3. From that site you can work out how bumpy the day is likely to be. If you select the Wind tab, it gives wind speed in a white circle, and gust speed in a red box. If the gust speed is around 3x the wind speed, this means thermals and thus bumpy conditions. Good for glider pilots, less good for a first flight.
4. What's missing is cloudbase - if the picture shows sun and cloud, this is unlikely to be a problem. If you see white or grey clouds with no sun symbol, the cloud might be too low for a pleasant flight. The RASP site
RASPtable, used extensively by glider pilots, lets you check forecast cloudbase among other parameters. I'd say anything less than 2,000ft is likely to be less than good for a first flight, though it might be perfectly flyable.
5. The final element is visibility - on some days it's like flying in the steam over a bowl of soup, and not great if you're flying for fun. XCWeather
Wind Map - Britain Forecast can give you this - anything less than about 5k visibility takes away some of the fun of a first flight.
Hope this is of some use.