Well, here are some things I've found to now:
Washington — June 14, 1920 Departure from the Zero Milestone
Sources: FHWA http://www.fhwa.dot.gov/infrastructure/zero.cfm (http://www.fhwa.dot.gov/infrastructure/zero.cfm)
Thomas L. Karnes. Asphalt and politics: a history of the American highway system. 2009. Page 76.
Ashland, VA — Source: Karnes, 77.
Richmond, VA — (June 15, 1920) Source: Karnes, ibid.
Oxford, NC — Source: Karnes, ibid.
Raleigh, NC — Source: Karnes, ibid.
Greensboro, NC — Source: Karnes, ibid.
Charlotte, NC — Source: Karnes, ibid.
Blacksburg, SC — Source: Karnes, ibid.
Athens, GA — June 28, 1920 Source: Karnes, ibid.
Atlanta — June 30, 1920 (two days + 3 days due to rain) Source: FHWA
Birmingham, AL — Source: Karnes, ibid.
Oxford, MS — Source: Karnes, ibid.
Memphis — Source: FHWA; Karnes, 78.
Detour through
Helena due to flooding of the Mississippi between Memphis and Little Rock. Source: FHWA
Note: This would have followed the Mississippi River Scenic Highway auto trail (Old US 61) to Dundee, TN, then across the ferry to Helena. The 1925 Rand McNally auto trail map shows the road curving north then south to the ferry, which was still a bit north of Dundee. The logical road for this would be Dundee Road, both because if its name and its shape. The crossing was likely at a place called Trotter Landing.
Brinkley, AR — Source: Karnes, ibid.
Ferrying across the White River in Arkansas — July 27, 1920
Sources: FHWA; Karnes, ibid.
Detour to avoid road construction between Arkadelphia and Fulton. Source: FHWA
Texarkana, TX — August 7, 1920 Source: Karnes, ibid.
Paris, TX — Source: Karnes, 79.
Bonham, TX — Source: Karnes, ibid.
Dallas — August 14, 1920 Source: Dallas, The Times Herald (http://freepages.history.rootsweb.ancestry.com/~jwheat/1920.html)
Fort Worth — depart on August 16, 1920 Source: Karnes, ibid.
Mineral Wells, TX — arrived on August 16, 1920 Source: Karnes, ibid.
Abilene, TX — August 20, 1920 Source: Karnes, ibid.
Trent, TX — delays on the way to Sweetwater due to rain and flooding.
Sweetwater, TX — August 24, 1920 Source: FHWA; Source: Karnes, ibid.
San Angelo, TX — August 25, 1920 Source: Karnes, ibid.
Note: The convoy bypassed the Bankhead route between Sweetwater and Pecos.
Fort Stockton, TX — Source: Karnes, ibid.
Pecos, TX — Source: Karnes, ibid.
El Paso, TX — Arrived September 8 and departed September 11, 1920 Source: Karnes, ibid.
Lordsburg, NM — September 13, 1920 Source: Karnes, ibid. (has August 13)
Silver Creek, AZ (east of Douglas) — Source: Karnes, ibid.
Douglas, AZ — Source: Karnes, ibid.
Tucson — September 18, 1920 Source: FHWA; Karnes, ibid.
Note: Scouts determined the Gila River crossings at Florence and near Buckeye were too sandy to cross, so Phoenix was skipped.
Ajo, AZ — Source: FHWA; Source: Karnes, 80.
Note: The Ajo route is not usually on maps of the Bankhead Highway, but the earliest Automobile Club map set I have for Arizona shows the maps: Yuma-Stovall, Stovall-Ajo, Ajo-(Comobabi), (Comobabi)-Tucson.
Sentinal, AZ — encountered heavy sand on the way to Wellton. Source: FHWA; Source: Karnes, ibid.
Wellton, AZ — Source: FHWA
Yuma, AZ — September 26, 1920 Source: FHWA; Karnes, ibid.
San Diego — Arrived on October 2, 1920, , Depart October 4, 1920 Source: FHWA
San Diego Union:
QuoteHeaded by the car occupied by Colonel Fletcher, Major Franklin and J. A. Rountree, secretary of the Bankhead Highway Commission and field director of the convoy, the procession wound slowly down into the city.
At Fourth and Walnut*, the convoy was met by motorized detachments representing the navy activities here, the army stations of Fort Rosecrans and Rockwell Field, and two naval bands . . . . The convoy went into camp in the park, north of the exposition buildings, and as the men turned out for "Assembly," Colonel Fletcher, introduced by the commanding officer, made what one dusty truck driver termed "the best speech of the whole trip."
Colonel Fletcher's speech was not oratory, nor intended as such. Simply and directly, he told the officers and men of San Diego's welcoming spirit and invited them to take part in the celebration planned in their honor. Applause such as only a crowd of army men can give greeted him as he told the men of the chicken dinner to which the American Legion last night invited them, of today's "launch ride" about the bay in a navy destroyer, of the free bathing privileges of the Service plunge and the auto ride about the city, planned for the enlisted men.
* There's a weird jog on 4th right at Walnut. I always wondered why it was there if 4th was the main road into downtown.
Whittier, CA — October 5, 1920 Source: Karnes, ibid.
Los Angeles, CA — October 5, 1920 Source: FHWA
San Francisco, CA — October 13, 1920 Source: FHWA