The Martin Luther King Jr National Memorial is the newest of the major monuments on and around the National Mall. It's located on the northwest bank of the Tidal Basin opposite the Jefferson Memorial and not far from the steps of the the steps of the Lincoln Memorial, where Dr. King gave his famous "I have a dream" speech during the 1963 March on Washington.
The $120 million project is an open-air memorial on a 4-acre site. Its centerpiece is a large statue of Dr. King, sculpted by Lei Yixin carved from Chinese white granite. The statue is surrounded by a large crescent-shaped area of landscaping combining stone, water, and trees. Other features of the grounds include a “Mountain of Despair,” symbolic of the struggle for civil and human rights. A piece of the Mountain of Despair has been separated to create the "Mountain of Hope," and from it emerges the figure of Dr. King standing, arms crossed, gazing out over the Tidal Basin towards the Jefferson Memorial. On either side of the statue is an Inscription Wall with extracts from Dr. King’s speeches and writings. The memorial sits on a direct line between the Lincoln Memorial and the Jefferson Memorial.
The official address of the memorial is 1964 Independence Ave SW, Washington, DC. The number 1964 was chosen as a nod to the 1964 Civil Rights Act.
Photos of the MLK Memorial
I have many more photos of the MLK Memorial here.
There is some parking next to the MLK Memorial along West Basin Drive SW, including some disabled parking spots. There's also a small parking lot on the eastern side of the Tidal Basin accessed along Maine Ave SW. (This parking lot is closed off during cherry blossom season.) There's more parking along the Potomac, extending all the way along Ohio Drive and up around Hains Point, including some convenient parking lots at the foot of the 14th Street Bridge.
When completed, the MLK Memorial will be an open-air space and accessible all day and night. There's generally no problem using tripods or flash, although being a new memorial it can get crowded.
If you want the sun on the front of the statue, go in the morning--the statue faces east.
Commercial shoots and filming may require a permit.