In Berlin, admission to museums is free on Thursdays four hours before closing. In Düsseldorf, you can take a one-hour Rhine cruise for $8; visit http://stadtfuehrungen.duesseldorf-tourismus.de.
The German National Tourism Office (New York, NY; 212/661-7200, www.cometogermany.com) offers more money-saving touring tips on its website.
Its webpage “Saving $$$ in Germany” lists itineraries that include hotel and meals for $100 per day or less. Also find cost-saving ideas, like the free city tours from New Berlin Tours (Auguststraße 5a, 10117, Berlin; phone +49 030 510 500 30, www.newberlintours.com).