Not actually "new"
Nové Město ("New Town") earned its name by being founded in 1348 as a planned extension of the medieval city, laid out by Charles IV around three large market squares — new relative to the Old Town next door, not new by any normal measure. It's the largest of Prague's historic districts, wrapping around the southern and eastern edge of the Old Town, and includes Wenceslas Square as its best-known feature.
Charles Square
Charles Square (Karlovo náměstí), one of the three original market squares and now more park than square, is the largest public square in Prague by area, though far less visited than Wenceslas Square nearby — a genuinely quiet, green spot in the middle of the city.
The Dancing House
Down toward the river, the Dancing House (Tančící dům) is one of Prague's few notable pieces of modern architecture, a deliberately off-kilter, twisting building nicknamed for its resemblance to a pair of dancers. It sits in deliberate, striking contrast to the baroque and Gothic buildings around it, and its rooftop bar is a popular spot for a river view from a different angle than the usual bridge and castle shots.
Municipal House and the National Theatre
Near the Old Town border, the Municipal House (Obecní dům) is a lavish Art Nouveau concert hall and civic building, worth seeing for its facade alone if you're not attending a performance. Along the river, the gold-roofed National Theatre anchors New Town's cultural side, with its own striking neo-Renaissance architecture.