Two medieval features dominate Prague, the Prague Castle which dates to 870, and the Charles Bridge (Karlův most) which dates back to the 1350's.
Prague Castle Complex is the largest in the world. Construction of St. Vitus Cathedral began in 1344. Inside the castle, the Golden Lane dates back to the 1500's. Alchemists, mystics, apothecaries, and castle guards all lived in the miniature houses on Golden Lane.
One of the most fascinating sights in Prague is the Astronomical Clock. As a center of learning, Prague was in the forefront of medieval physics and astronomy. Built in 1344, the clock tells time, track sunrise/sunset, phases of the moon, and more.
En route to Vienna, a quick stop at Kutna Hora was a pleasant surprise. Away from the cities, you see more of the original Bohemia and, of course, fewer English speakers!
Vienna, the grand capital of the Habsburg Empire, is dominated by the monarchy. The Schönbrunn palace (all 400 acres of it) sits just outside the central city and was the summer palace for monarchy. The Imperial Palace in the city center houses the beautiful Austrian National Libary and the Imperial Treasury houses jewels and reliquaries dating back to the time of Christ.