The Chopin Museum is the bane of my touristic experience here in Warsaw. I have tried numerous times to come to this museum but they are always sold out of tickets or run out of tickets on free entry day. So I have yet to visit it so this isn't a plug just yet..
However, a good tip is that they offer return bus trips to Zelazowa Wola, Chopin's birth place and home, every day departing at 10 am and noon (during the week, they mostly just depart at noon) for 30 zloty. This is a good deal because the train takes you to the biggest town near Zelazowa Wola and costs over 15 zloty one way plus the extra waiting time and cost to get to the actual museum (please note that at the museum they did not have information about the buses to Zelazowa Wola in English so please inquire at the guest desk).