Popular museum for cloth
If you can catch this museum when it is open, it has fascinating fashion expos. from July - October 2014, there is an exhibit on 50s fashion starting right after the end of WWII, and including a plethora of fashion designers such as Jacques Fath, Jacques Heim, Christian Dior, and tid bit of Channel.
Beautiful, small (?) palace in the 16th. I saw the 100 Years of Conde Nast Fashion Photography exhibit there, and it was beautifully done (May 2014). A nice area to stroll around, make your way to the fancy hotels, and have an expensive cocktail. Fair warning that almost nothing else is open on Sundays in that area.