Built as a private home, 6720 Sunset Boulevard became a bungalow court in 1922. Thie following is my original research. The above image is from the California State Library.
The residence was built on the south side of what was then the 500 block of West Sunset Boulevard (West Sunset began west of S. Cahuenga) midway between Las Palmas (then Estelle Avenue) and Townsend Avenue (later McCadden Place).
Built c. 1905-1906 as the country home of William A. and Sarah Avery, it was known as “El Nido.” Avery was president of the Western Paper and Bag Company. He died in 1908.
From August 1911-August 1912 the Robert. V. and Lulu Foster family of Long Beach rented the “old Avery Place” (old being a relative term in Hollywood), described as a “large, beautiful country house.” During the Fosters’ time here, the houes of West Sunset were renumbered going from 3-digits to 4-digits, continuing the sequence from east of Cahuenga. The old Avery place became 6720 Sunset.
After the Fosters, in 1914, the old Avery place was rented by the Franklin A. and Florence V. McAllister family. Like the Fosters, they were not here long.
6720 Sunset often sat vacant until 1921 when it was purchased by Edmund L. and Blanche Schultz. E. L Schultz had owned a drugstore chain in Denver. The couple and their daughter Jane came to Hollywood in 1920 after his retirement.
In early 1922, Blanche commissioned contractor F.W. Hicks to build cottages on the parcel to create a bungalow court.
At this time, the former private residence on the corner of Sunset and Las Palmas, recently taken over by the Screen Writers Guild as a clubhouse, was renumbered from 6716 Sunset to 6700 Sunset. The Schultz parcel took over the addresses 6712 to 6724 Sunset.
Schultz had three 2-family 1-story bungalows and 1 2-story single-family cottage built on the east side of the parcel, facing west. The first duplex unit, closest to the street, was addressed at that time as 6712/6712-1/2 Sunset; south of that unit was 6614/6614-1/2 Sunset; south of that was 6616/6616-1/2. At the end of the row was 6618 Sunset, the single-family cottage. The auto garage (addressed then as 6722) were at the east-rear corner of the parcel. Along the east property line was a fourth duplex, addressed as 6722-6724 Sunset.
The bungalows were rented as homes, not for transient guests. 6700 itself continued as the Shultz’ private residence into 1924.
In March of that year it was reported that H.C. Blumenthal had taken out a long term (99 year) lease on the property and intended to build a high rise apartment building on it. It was never built.
Schultz remained the owner of the property, though they lived elsewhere. Edmund died in 1941, Blanche in 1945. Their daughter, Jane Sewell, became owner of the property and retained ownership into 1951 at least.
Over time there were changes. The old Avery residence was converted into apartments and its address became 6722 Sunset; as of 1950, the apartments were numbered 6722-1/4, 6722-1/2, and 6722-3/4. The 2-story cottage became 6620, and cottage #3 became 6716/6718 Sunset. The cottages on the west side of the parcel became 6624/6624-1/2. Owners after 1950 made further alterations, such as converting some cottages into commercial spaces and changing duplexes to single-family use.

Detail of the 1950 Sanborn Fire Insurance Company map for Los Angeles County. Compare to the 1913 map above. LOC.

More detail from the 1950 Sanborn. The smaller auto garage at the back of the parcel was added by Schultz in 1921 before the bungalows went up. LOC.
In Fall 1951, Ernest Forssgren, owner of 6700 next door, split his pacel in half north to south and demolished the front of the building that occupied it. The back half of the building (an auditorium addition dating to 1922 that now housed a tv/radio school), remained in place and was readdressed as 1447 Las Palmas. By 1952, Forssgren was also owner of the bungalow court. The two properties formed an L-shaped parcel with frontage on Las Parmas and Sunset.
In January 1954, the property, which now included 6720 and 1447 North Las Palmas, was sold at auction.
Alterations were fairly minimal. A low wall was erected along the Sunset frontage, which was later replaced by a tall breeze-block wall. In 1958, a swimming pool was installed near the west rear corner of the parcel. It became the Hollywood Center Motel around that time, addressed as 6620 Sunset. 1447 North Las Palmas became the Hollywood Center Theater. See my post on 6700 Sunset, here.
The property remains remarkably intact today.