As far as I know you need to pay admission to use any of the toilets here. There is a suggested donation but if you are really in need you can just choose to pay nothing and you will be let in. The closest bathrooms to the entrance are on the north end (the right hand side as you enter the building) of the main atrium just past the first exhibition room. Venture further in to the museum for more hidden and less busy bathrooms.
Mon: Closed, Tues–Thu: 9:30 a.m.–5:30 p.m., Fri and Satu: 9:30 a.m.–9:00 p.m., Sun: 9:30 a.m.–5:30 p.m.