In the 15th century, the Nieuwmarkt was just that - a market, but it did not take on the name until the 17th century when it was incorporated into the city. It still has a fine collection of old houses although many were demolished when the metro was built in the 1970s. The square is dominated by the Waag, the old weighhouse.
Nice cafe terraces in the summer, and restaurant Bern is still the place to go for a proper fondue. You need to book.