If you want to know more about the history and culture of the area, these are helpful documentaries and movies:

Eyes on the Prize

Multi-part PBS documentary about the Civil Rights movement. Superb archive footage and insightful interviews. A must-see. Aired on public television in 1987 and was finally released on DVD in 2010.
http://www.shoppbs.org/eyes+on+the+prize

Boycott

Well-told drama about Martin Luther King Jr. (Jeffery Wright) leading the sanitation workers strike in Montgomery, Alabama. (2001.)
http://www.allmovie.com/movie/boycott-v234660

Respect Yourself: The Stax Records Story

Music-filled documentary about the rise and fall of Stax Records and its important place in the history of American soul. Narrated by Samuel L. Jackson. Highly recommended for the archive footage of all the big stars like Otis Redding, Booker T. & the M.G.’s, Sam & Dave, Rufus Thomas, The Staple Singers, Isaac Hayes, and many more! (2007.)
http://www.amazon.com/Respect-Yourself-Stax-Records-Story

West of Memphis

Director Amy Berg’s documentary examines the West Memphis Three–teenagers who seemingly were falsely convicted for the murder of three little boys. (2012.)
http://www.allmovie.com/movie/west-of-memphis-v553701/

Let Freedom Sing


Chronicles the power of music that helped move a generation during the Civil Rights Movement. Features 29 inspiring performances including Respect, Change Is Gonna Come, People Get Ready, Fight the Power, and What’s Going On.  (2009)
http://www.allmovie.com/movie/let-freedom-sing-how-music-inspired-the-civil-rights-movement-v482106

Elvis: Return to Tupelo

Features interviews with childhood friends, first girlfriends, and early bandmates to build a complete picture of the well-mannered Southern boy with a talent for singing.  It’s the story of Elvis’s dirt-poor upbringing in Tupelo, MS, his job as a Memphis truck driver with musical aspirations, and his rapid rise to stardom in 1956.  Even if you know a lot about Elvis, this documentary is still full of surprises. (Elvis was actually blonde!) (2008.)
http://www.amazon.com/Elvis-Return-Tupelo-Presley

Other movies filmed in Memphis and nearby:

21 Grams (2002)
3000 Miles to Graceland (2001)
The Angel Doll (2000)
Black Snake Moan (2007)
Cast Away (2000)
The Client (1994)
The Delta (1996)
Elizabethtown (2005)
Elvis (2005 TV Movie)
Elvis and Me (1988)
A Family Thing (1996)
Finding Graceland (1998)
The Firm (1993)
The Grace Card (2011)
The Gun in Betty Lou’s Handbag (1992)
Forty Shades of Blue (2005)
Great Balls of Fire! (1988)
Heart of Dixie (1989)
Highway 61 (1991)
Hustle & Flow (2005)
Leningrad Cowboys Go America (1989)
Making the Grade (1984)
Memphis (1992 TV Movie)
Memphis Beat (TV Series)
Memphis Belle (1990)
Mystery Train (1989)
Nothing But the Truth (2008)
A Painted House (2002)
The People Vs. Larry Flynt (1996)
The Rainmaker (1997)
The Silence of the Lambs (1991)
Soul Men (2008)
Take Me to the River (2014)
This is Elvis (1981)
Trespass (1991)
Tricks (2007)
Walk the Line (2005)

The Internet Movie Database (IMDb) has a complete list of movies filmed in Memphis:
http://www.imdb.com/search/title?at=0&locations=Memphis,%20Tennessee,%20USA&sort=moviemeter,asc