Sure, restaurant signs are a common thing around the world. (Even the Romans had them.)
But the historical background of such signs is slightly different here in Switzerland. Being a Germanic culture, hospitality has always meant “no strings attached”. In other words, hosting someone was not done with a commercial intention.
Back in time, there were no street names or numbers for someone to navigate through a town. Instead, each house has its own name. So when it came to picking a name for a tavern or a drinking hole, the name of the house was often adopted. (For proof, look around a typical Swiss old town and you will see plenty of houses with names painted on them.)
But why the star as a sign for a restaurant?
There is an easy answer: The star was a symbol for the guild of brewers, and it was considered a lucky charm. Starting in the 13th century, when there was a batch of fresh beer at a tavern, the restaurant owner (who was also a brewer) would hang a sign outside to attract customers: A star, or “Stern” in German.
Still today, there are 230 Swiss restaurants carrying the name “Sternen”, putting it in fifth place after “Rössli”, “Bahnhof”, “Löwen” and “Kreuz”.