On trans-pacific airways the 2707-300 suffers from its limited range, 4000 miles at best. The main airway is obviously L.A - Tokyo. There is no other solution than to make a stopover. I thought Hawaii was the only option, but Anchorage is actually closer, and the entire trip far shorter !
Once again, the key is Mach 2.7. They did tried Concorde on trans-Pacific, but a 747 without a stopover did a job better (how surprising !).
At Mach 2.7 however it is a different matter, and the 2707 saves some time.
I can see a SST lifting off from Tokyo, fly to Anchorage, and then fly along the western coast, either to Seattle or to L.A or San Fransisco. The trick is to fly far enough from the coast so that the sonic boom is confined to the Pacific ocean.
This is a useful website to plot air ways.
https://www.distancefromto.net/
Tokyo - Anchorage is 3500 miles (2 hours flight)
From Anchorage
- Seattle: 1460 miles (note: Tokyo - Seattle, direct, is 4800 miles: too long)
- San Fransisco: 2042 miles
- Los Angeles: 2334 miles (1h:30 mn)
Now through Hawaii / Honolulu
Tokyo - Honolulu: 3870 miles (let's say three hours including the stopover)
Honolulu - L.A: 2570 miles
Honolulu - Seattle: 2675 miles (1h:30 minutes)
Now how about Australia ? forget Anchorage

and the distance from Hawaii is too long, 5000 miles. The trick is to replace Hawaii by French polynesia - Tahiti, with the capital Papaete.
Los Angeles - Tahiti is 4125 miles, at the aircraft extreme range.
Tahiti - Sidney is 3800 miles.
Tahiti to Auckland is only 2500 miles.
Concorde initial range was 3600 miles, but some tweaking here and there resulted in flights as far as Barbados, 4200 miles from London. I can see the 2707 evolving like this.
for the sake of comparison Mach 2.7 is 1800 miles an hour. Hence the 2707 can cover 3600 miles in only two hours.
Most of the distances above are more or less 3600 miles, two hours of flight time.
Which mean trans-Pacific flight times are cut to 5 hours (including the usual 1h stopover).
finally, with 250 passengers, the 2707 is not unlike an A330 or the earlier 747SP and A300.