Athens was a small village well into the mid-19th century, and did not begin to grow until it became capital of Independent Greece in 1834. It's hard to believe in today's traffic-clogged Athens, but the Byzantine Museum, at 22 Vas. Sofias, occupies the Renaissance-style villa that the Duchess of Plaisance built -- imagine this, in today's Athens -- as her country retreat in the 1840s. Several other buildings from the same period, including the Parliament House (the former royal palace), the Grande Bretagne Hotel (a former mansion), and Schliemann's house, the Iliou Melathron (see the Numismatic Museum, above) are still standing in Syntagma Square. Unfortunately, all too many of the neoclassical buildings built in the 19th century were torn down in Athens's rapid expansion after World War II. Here are a few suggestions of some buildings you may pass on your explorations of central Athens.
In the Plaka, several 19th-century buildings have survived, tucked between the T-shirt shops and restaurants on busy Adrianou (Hadrian) and Kidathineon. 96 Adrianou is thought to be one of the oldest surviving prerevolutionary houses in Athens, dating from the Turkish occupation, and the nearby 19th-century Demotic School has a pleasant neoclassical facade. Over on Kidathineon is the house in which mad King Ludwig of Bavaria stayed when he visited Athens in 1835 (there's no number on the house, but a small plaque identifies it), and several other buildings here are former houses from the same period.
Finally, if you climb up through the Plaka to the Anafiotika district on the slopes of the Acropolis, you'll find yourself in a delightful neighborhood with many small 19th-century homes. This district is often compared to an island village, and small wonder: Most of the homes were built by stonemasons from the Cycladic island of Anafi, who came to Athens to work on the buildings of the new capital of independent Greece.