While Memphis is full of musical must-hit history from Sun to Graceland and Beale Street, probably the most interesting stop for teens is Soulsville USA, also known as Stax, the Museum of American Soul Music. 
The tour at Stax starts in a country church — Photo courtesy of Stax Museum of American Soul Music The artists from Stax include Aretha Franklin, Isaac Hayes and David Porter, and even Elvis Presley - but it's the influence of this tiny label that will carry the most weight with teens. Both Justin Timberlake and Three Six Mafia, among others, claim plenty of Stax soul in their music. The museum traces the roots of soul music from the tiny churches of the Mississippi Delta to the city, and treats visitors to slices of some of our country's most famous tunes.
If your teens are truly into music, then a visit to Graceland should be part of your day (or could be almost a whole day depending on their interest). Seeing Elvis's home in its 1970's splendor is a treat, but the real connection comes from discovering how a really shy kid used music and flamboyant clothing to create a true cultural phenomenon, pre-social media.
Your teens have probably studied the Civil Rights Movement in their high school history classes or seen it portrayed in everything from 42 to The Help. But nowhere does the true emotion and incivility of that time come to life better than at the National Civil Rights Museum, housed in the former Lorraine Motel, site of the assassination of Dr. Martin Luther King, Jr. 
The Lorraine Motel, site of the King assassination and now part of the National Civil Rights Museum — Photo courtesy of Memphis Convention & Visitors Bureau Many exhibits show how teens and young adults of the era were involved in the movement, on both sides, and paint a very real picture of how the fight for civil rights is far from over - and still relevant in the world today.
If your kids want to work out, there's no better place than taking a jog along the Mississippi or the Greater Memphis Greenline, which stretches along the particularly scenic section on the Wolf River from Shelby Farms to Midtown. If they're into sporting events, there's the NBA's Grizzlies and the minor league Redbirds, who call the very cool AutoZone Park home during baseball season.
And teens though they may be - what kid doesn't love a zoo? The Memphis Zoo has incredible exhibits that allow visitors to get very close to many of the animals, and features panda, polar, and grizzly bears as a few of the main attractions.
For meals, be sure to try some of the city's best barbecue - you can't call a trip to Memphis complete without it. On the near east side, High Point Pizza is a great neighborhood choice (but know that the dining room is pretty small - fortunately there are outdoor tables, weather permitting).