Full details are in Robert L. Karg and James L. Thompson, A Heuristic Approach to Solving Traveling Salesman Problems (Management Science, 10(2):225–248, 1964). The PDF is available from JStor and Informs.org (both paywalled). This is the paper that produced the optimal tour of 10,861 miles. It also includes the full distance table but I'll not reproduce that here as it's way too much typing.
The solution is also illustrated on page 15 of The Traveling Salesman Problem by David L. Applegate, Robert E. Bixby, Vasek Chvátal and William J. Cook (Princeton University Press, 2007). The introduction to that book, which includes the relevant page, is freely available from the publisher.