In the above map from early 1600 you can see an outline of the planned development for the city of Amsterdam. Eventually being surrounded by 26 Windmills at the city wall, keeping the land dry and water fresh. In the same period Dutch had settled on the island of manhattan and were building ‘New Amsterdam’. Typically the city streets were also named after streets which originated from Amsterdam like Broadway for instance. As the name implies, still today is a wide avenue in New York City. The name Broadway is an English translation of the Dutch name, Breede weg. A stretch of Broadway is famous as the pinnacle of the American theater industry.
Some of the similar streetnames and typical Dutch names that one could find in Amsterdam and New Amsterdam during that time were:
De Heere Straet (now Broadway)
Het Cingel (now Wallstreet) on the ouside of the wall called Nassau st.
The Plein (now Bowling Green)
Heere Gracht (now Broad st.)
Noort Rivier (now north river)
Prince Straet (now Beaver st.)
Begijn Gracht (now Beaver st.)
Paerel Straet (now pearl street)
Het Marckvelt (now whitehall st)
Harlem Meer (from Haarlemmer Meer)
Brugh Straet (now Bridge st.)
Stadt Huys Laan
Broadway originated as a Native American trail called the Wickquasgeck Trail, which was carved into the brush land of Manhattan. This trail originally snaked through swamps and rocks along the length of Manhattan Island. Upon the arrival of the Dutch, the trail soon became the main road through the island from New Amsterdam at the southern tip. The Dutch explorer and entrepreneur David de Vries gives the first mention of it in his journal for the year 1642 ("the Wickquasgeck Road over which the Indians passed daily"). The Dutch named the road "Heerestraat". diverted from the similar called canal in Amsterdam.
Later the settlements of Harlem (Haarlem) and Brooklyn (Breukelen) were founded. In the image below you can get a good idea of how big New Amsterdam was at the time. You can see the new city’s grids in the background.