Carre D'or is the eastern part of Grande Île and not as crowded as the central and western part of the island. Here you'll still find narrow streets and half-timbered houses. A central location you should definitely find while exploring Strasbourg is Place Saint-Etienne. From there you can then continue to Neustadt.
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Place Saint-Etienne is a square you should visit. It's small and cozy, and it's surrounded by half-timbered houses.
A great example of the half-timbered houses you'll find here!
Rue de l'Arc-en-Ciel.
Rue des Veaux.
Place Saint-Etienne again.