Clearly this is the time to see what the Duke Ellington School of the Arts is all about -- both teachers and students are showing around town. The faculty show opened yesterday at the Foundry Gallery (404 Seventh St. NW), featuring sculpture, paintings and photographs by seven faculty members. The Ellington students are showing at the student gallery in the Corcoran School of Art, through June 17. The Shows of Summer

As thoughts turned to summer over the holiday weekend, Washington galleries were gearing up for exhibitions designed to attract not just stalwart Washingtonians trapped on the good ship "Humidity" but the thousands of young art lovers who invade the city for summer internships.

"New Talent," at 14 Dupont Circle-area galleries, will show just that. Everyone from L.A. photographers to emerging Washington painters and sculptors will get some exposure this summer at Addison/Ripley, Wallace Wentworth and 12 others in between, beginning June 29 and running through July. For more information, call Kathleen Ewing at the Kathleen Ewing Gallery (328-0955). Art, Etc.

President Reagan this month appointed Naomi Zeavin, president of UR Unique, a public relations firm, and a former author, actress, and producer and director for public television, to represent the state of Virginia on the President's Advisory Committee on the Arts at the Kennedy Center. Charles Camalier Jr. represents Maryland, and Richard Taylor the District of Columbia . . .

"Discover Graphics," an exhibition of area high school students' etchings, opens at the National Museum of American History Saturday . . . The kineticism of Glen Echo Park Gallery will go on display in "Moving Parts," an exhibition of sculpture, assemblages and mobiles opening Friday . . .

"Aspects of a Southern Story" is a free joint poetry reading by Robert Sargent, Shirley Cochrane and Hastings Wyman Jr. at the Market Five Gallery in Eastern Market (Seventh Street and North Carolina Avenue SE) . . . One of many alternatives to the Corcoran's "Washington Show," the "Salon de Refuses" opens Tuesday at the Washington Women's Arts Center, Lansburgh Cultural Center (420 Seventh St. NW).