Part of the Smithsonian Institution in Washington DC, this is the only US museum dedicated to both historic and contemporary design. Housed in the 64-room mansion built by billionaire Andrew Carnegie in 1901, the 210,000-piece collection offers artful displays spanning 3000 years over three floors of the building. The beautiful garden is open to the public and accessible from 90th St or from inside the museum. Free tours are at 11:30am and 1:30pm on weekdays, and at 1pm and 3pm on weekends.
Technology is a big feature of the museum. Some exhibitions have interactive touch screens or huge digital design tables that allow you to create your own works using a nifty electronic 'stylo' and save them to a website for later retrieval. The same pen can also be used to save your favourite exhibits to an online lookbook; you'll be given it upon entry. There’s also a problem-solving Process Lab and a mesmerizing Immersion Room, where you can project images onto the walls from patterns dating back to the 18th century.
Check out the museum's design store before you leave. There's also a cafe. Note that it's a couple of dollars cheaper to buy tickets in advance online.