Mobile Phone : Courier - Couriers or runners can be found on every bustling metropolis street corner. For a few coppers they will carry a written (or spoken) message to any inhabitant of the city. If that person is at home you may even get a quick return message. If you want a message or maybe even a package sent to a nearby town it will cost you quite a bit more depending on the distance and weight.
The couriers can be anything you like, street urchins, mundane or magical creatures like pigeons or fairies. Longer distances can be covered by horse riders or if speed is the essence and you have a highly magical world, by means of teleportation, magic carpet or even by air elemental.
Clock : Muezzin - Time is money and people have always been willing to pay handsomely to know what the time is. This could be handled either by the state, church or by an enterprising candle maker as a municipal function. Water clocks existed in many different cultures around the world from as early as 4000BC, all you need is a regular sized vessel with a regular sized hole in it and are easy to manufacture by potters or smiths using templates. In my Arabian setting this function was performed by the muezzin who called the faithful to prayer but I added a rudimentary clock to each minaret in the form of 12 metal fish which would tip down to strike the hours (the time was referred to as 3 fishes or 4 and a half fish). Sundials (shadow clocks) can be erected as municipal features, like Egyptian obelisks, or complex architectural as is the case with a stone circle like Stonehenge.
News Media : Town Crier - This function can be performed by a Town Crier or similar who at various times of the day (he also performs the function of municipal clock) cries out the latest public announcements and for will cry private announcements such as market day announcements, weddings, birthdays etc. It is also the function of the Town Crier to "post" written versions of these notices on a notice board.
Fridge : Windcatcher - There's nothing like having a cold beer after a strenuous days adventuring, In temperate regions that function might be performed simply by using a cellar but in hotter climes they use a windcatcher or "Malqaf". For hundreds of years these towers have been designed into Persian buildings as a form of air-conditioner which uses the Coandă effect to cool the air. If coupled with an underground canal or resevoir they can chill water down to near freezing temperatures. The Persians built this feature in to their ice houses (Yakchal) for this express purpose. Or you could use a captive immature frost giant...
