score:37
The linked Smithsonian page also has this page from a report, which expresses it a bit more explictly:
...completed an earthbound journey of nearly 14,000 miles by land, visiting the capitals of the 48 contiguous states and the District of Columbia. The mobile display completed the tour travelling 12,000 miles by sea, for visits to Honolulu in April, 1971, and to Anchorage, Alaska's first city, in May.
So the missing one is indeed Juneau. I agree with your suspicion that it probably comes down to Anchorage being a much more accessible location for most Alaskans.