Witness the most picturesque enclave in all of Amsterdam farther north on Voetboogsteeg: the Begijnhof, whose private residences nestle around an inner court. The handsome wooden house at number 34 is one of only two that survive below the river IJ.
Follow the Oudezijds Voorburgwal up north to Oudekerkplein (Old Church Square), seat of the monumental Oude Kerk, consecrated in 1306. At the north side of the square is the Museum het Rembrandthuis, where the artist lived in his heyday; here Rembrandt's masterpieces are superimposed on a superbly restored interior.
By now you've probably realized that you're in Amsterdam's fabled red-light district, De Wallen. Adults with a sincere curiosity about the sex trade in the Netherlands can take a non-sensationalistic tour of De Wallen with a former sex worker. Or you can climb up to the splendid attic church concealed in an ordinary house at Ons' Lieve Heer op Solder ("Our Lord in the Attic"), where persecuted Catholics worshipped in the 17th and 18th centuries.
Round off your first 24 hours in Amsterdam with a typically Dutch supper: the Pannenkoekenhuis Upstairs at Grimburgwal 2, one of Amsterdam's best pancake restaurants, where savory pancakes are doled out in a tiny but convivial space. Think pancakes are just for breakfast? Sample the irresistible fondue at Café Bern (Nieuwmarkt 9), which serves Swiss specialties in a typically Dutch bruin café interior.