It says San Francisco on the wall above the ticketing counter.
"Barack Obama Sr. poses with his son in the Honolulu airport during Obama Sr.’s only visit to see his son while he was growing up in Hawaii. Young Barack was in the 5th grade when the photo was taken. (Photo courtesy of Barack Obama / March 23, 2007)"
Something very strange is going on here. The San Francisco sign is so easy to see in that picture of him with his father. The one with Barack Sr. and Ann the wording above is very hard to read. I guess since the angle is slightly different could make it harder to read. But could it say "Philippines" like you thought it said in the one picture and also "San Francisco"? I am not familiar with airports.
I found this archive picture of the Pan Am ticket lobby at the Honolulu airport from 1961 (at this link of Hawaiian aviation historical photos). Note that the San Francisco banner is actually a counter sign hanging from the pole seen on the left. If you click on the preview picture at the site, you can see a full-screen version of the picture.
This may be a different part of the terminal, but it sure looks to me like it's absolutely the Honolulu Airport in the 1960's.
On another note, regarding the 1964 divorce reference to a marriage on Maui in Feb 1961, if you click around on the site linked above, it looks like air travel to Maui was pretty primitive in those days. What did it cost to fly to Maui in 1961, and where would one go near the few airports that were there? I'm assuming the husband had the resources for the trip, since I'm not sure that a 18-year-old would.
-PJ