Poland's capital, Warsaw, with close to 2 million inhabitants, is one of relatively few places in the Baltic and Central Europe region with a "big city" feel. Start your visit by getting your head around the Old Town center, alone offering plenty to keep you busy.
One half of the Old Town centers on the Old Town Square (Rynek Starego Miasta). Like some 85% of Warsaw,many of the buildings here were damaged or destroyed during World War II, and you can see fascinating displays of how carefully and professionally they were reconstructed (many in the 1950s) in the Warsaw Historical Museum, which occupies several of the buildings fronting onto this square.
Not far from this square, you'll find several museums devoted to famous Poles. The first is Marie Curie, who was born in Poland, and the Marie Sklodowska-Curie Museum is just north of the square, enroute to the New Town. Secondly, you'll see the Adam Mickiewicz Museum of Literature on the square. While you may not know much about writer Mickiewicz before you travel to Poland, you'll soon get used to seeing his name and statue everywhere.
The second major half of Old Town can be found at the Castle Square (Plac Zamkowy). Basically every building that fronts this square was rebuilt from the ground up after the war, and you'll see that by and large a good job was done; enough that it found a place on UNESCO's World Heritage list.
The Royal Castle is the main sight to see on Castle Square. Its origins were in the 13th century, but after a long history of extensions and the finality of World War II damage, it was eventually entirely reconstructed in the 1970s and 1980s. It may not be original as such, but it's still magnificent and stands proudly on Castle Square.