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​The best thing to do is to join a free tour around the Old Town in Warsaw that is organized every day. It is free of charge but they expect to be tipped at the end of the walk. They are cool:-) You will find more details on the tours here:  
They do also the Jewish part of the city and communism theme too.
If you start with them they will mention a lot of things to see and you can decide what next.

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​On rainy days or when you have already made long walks in the streets of Warsaw there are bus city tours that might help to explore the city further. Hop on Hop off buses run daily and are not weather dependant. You can enjoy sight seeing while sitting on the upper deck.