I visited the Zürich Landsmuseum with my parents when they were over a couple of weeks ago. The Landsmuseum is one of several Swiss national museums and is definitely worth a visit. The entrance fee is not too steep at CHF10 and you do get your money's worth. One afternoon is not enough to see everything though so if you can afford it, go to the museum several times to visit each section separately.
The museum is housed in this wonderful building less than 5 minutes walk from Zürich HB (the main train station). No cameras were allowed inside so I can't show you what it looks like inside but the museum website (available in English) does have photos of the different exhibitions.
The permanent exhibition "History of Switzerland" present Swiss history from its beginnings to the present, and give an insight into Swiss identity and culture. We then moved to another permanent exhibition "Swiss Furniture and Interiors" that presents interiors and furniture from the museum’s own collection. I especially liked the reconstructed period rooms. My Dad then insisted on going around the the Armoury Tower which also houses collection of costumes and traditional garments.
By that point, after 4 hours, I was getting a bit desperate to go home although there was plenty left to be seen. I'll go back!!