The Old Town (Polish: Stare Miasto or Starówka) is Warsaw's most distinguishable area, which once was the city center. It is fully contained within the boundaries of Śródmieście, the most central district of Warsaw.
This itinerary takes you for a walk around the Old Town. It should be fully manageable to see all the sights within a day, although more time may be needed if you plan to traverse all the exhibitions at a reasonable pace.
If you still have some time the same day, you can then visit the New Town (Nowe Miasto), which — contrary to what the name suggests — is basically another old historical city area, just north of the City Walls. The Royal Road also begins here, but you'll be better off leaving it for the next day.
The Old Town was obliterated in 85% during World War II. Most of the present-day buildings were carefully reconstructed in the 1950s. The castle was rebuilt even later for political reasons and has regained the adjective «royal» only after the fall of communism.
Get a free map of Warsaw with the transport routes from the Tourist Information at ul. Krakowskie Przedmieście 39 (9AM-8PM; Oct-Apr: 9AM-6PM) or many other places.
There is a shortage of public toilets in the area. When in need, search for a bar or a restaurant as they are obliged by the law to have toilet facilities. Sometimes, they may be for customers only but it doesn't hurt to ask.
Warsaw is generally a safe city and the tourist areas are particularly well-patrolled. There are however pickpockets operating, so watch out, especially in the crowded places.
Should something bad happen, call the police (policja) at 997 or 112. They used to have a problem with interpreters but hopefully it has now been solved and there is even a tourist emergency freephone operating Jun-Sep 10AM-10PM at 0 800 200 300 (or +48 608 599 999 from a mobile phone) where you can communicate in English, German or Russian.