Omnes viae Romam ducunt / omnibus viis Romam pervenitur
I think it's rather "Romam", not ad Romam, because I've found 2 expressions, but I couldn't explain why, maybe because of the verbs ducere, and pervenire.
Via is more like a way, it can be used in the metaphorical sense, platea is less abstract I think.
Usually, streets are in towns and cities. Roads form the arterial links between centres. That said, the ancient Roman road between Canterbury in Kent and St Albans in Hertfordshire is Watling Street, which I have always found odd. The definition of a street usually recognises that it is lined with buildings, and is therefore predominantly urban. Of course, many old roads are now lined with buildings because of ribbon development, so the lines are blurred. That still does not explain Watling Street, though... does anyone know why?