Typically, the sightseeing of Warsaw starts and ends on the left side of the Vistula river. But if you happen to arrive a day earlier or depart a day later, consider taking some time to cross the river and explore the less touristic side of Warsaw. Here's a short video that will give you an idea of what can be found just across the Poniatowski bridge.
It's hard not to notice the National Stadium, which nowadays is very modern and impressive. But we still remember the former 10th Anniversary Stadium, which used to be located here. Built in the 1950's, it was the main venue for state festivities and important soccer and athletic competitions. Because of technical problems, in 1983 the stadium was abandoned and started being reclaimed by nature. In 1989 the city turned it into an open-air market with traders not only from Poland, but also from abroad. The stadium had a bad reputation because of its connection to the black market. Eventually, the stadium was demolished and a new stadium was built.
Most tourists visit the Royal Baths or Wilanów, but very few have heard about the Skaryszewski Park, which is an English-style park, one of the most beautiful parks in Warsaw especially in the summer). It is also a very popular venue for wedding photoshoots. If you're looking for a place to relax, we definitely recommend visiting it.
Just next to the park, on the other side of the biggest of its lakes, you'll find the best-smelling place in Warsaw, the source of heavenly sweetness: the Wedel factory. Once a year, during the Museum Night, it's possible to explore the factory and see how the delicious Wedel sweets are made (however, the amount of tickets is limited, so it's quite hard to get them). On other occasions, you can visit the shop next to the factory and try their exquisite liquid chocolate. (To learn more about Polish sweets and treats, see The Sweetest of Poland)
If you have more time to go deeper into the right-bank side of Warsaw, explore the fascinating Praga district.