I know where my local transmitter is and I needed a roof aerial years ago and could see line of site to the mast. 20 -30 miles I suppose for a good signal though some stations are deliberately low-powered for a particular audience, but built-up areas and hills can cause a problem...
Rocky, I've just bought a very cheap dab radio for my bathroom from Argos for 12.99 .... should have been 16.99. It's a great little radio ( 181 reviews on it ) ... Argos value range 911/ 9822