> I live in a big city, it could be raining frogs in one part and a happy sunny day in the other and the best thing any weather report could say to me is 'expect rain'.

Just in case you haven't seen it: some services provide conditions and forecasts for particular locations with better resolution than ‘the city’, and can show the projected movement of rainclouds.

(You'll have to research the services for your country yourself, as I doubt it that my local one is useful for outsiders. But I'd guess that these days many big web services have these features.)

Well, I have such service, though it's a map with the current rainfall data.

Still, after I wrote the previous comment the rain has come. And in 15 minutes there was no rain and the sun shone brightly and in another 30 minutes even puddles all dried up. So the practical usability of such service is quite limited.

I occasionally amuse myself by gawking at the formations of rainclouds in my vicinity, which included stuff from thunderclouds thousands of kilometers across, to jagged clouds bringing alternate rain and sunshine, to again a massive cloud covering this whole region except a circle right around my house. So I definitely can recommend finding such a service with cloud movement and with projection of it into the future—if only for the curiosity value.

The one I use is https://yandex.ru/pogoda/maps/nowcast — but I'm not sure if it works in English, and these days perhaps one will prefer not to use Yandex anyway.