How is this second use of 'such' any different than the first use of 'such' in the same sentence?
Such is not a pronoun here. It acts similar to a determiner or an adjective. The OED calls it a "demonstrative word". The unabridged Merriam-Webester calls it an adjective. The noun you ask about is there: place. The exact phrase "travel to such place" appears in the 1999 Charter of the City of Los Angeles. This is 49 years after its use in the Truman order.
If a Retired Plan Member resides outside of the State of California, the Board shall have the authority to order medical examinations of Retired Plan Members at any place it may determine to be desirable and shall, if it is determined that it would impose hardship on the person to be examined to travel to such place, have the authority to defray...
In addition a 2005 Code of Federal Reguations (link) also includes the phrase:
...that a total of one-half hour or more is required for the auditor to travel to such place and back to the headquarters, or to the next place of assign-
Given that neither the Charter nor the Code of Federal Regulations is subject to any such thing as telegraphic language, one can assume that such place is a phrase happily associated with government communications of many different kinds.
Granted there is a named antecedant ('any place') in the Charter, yet the OED gives definitions for the adjective/demonstrative such that include both
1 Of the character, degree, or extent described, referred to, or implied in what has been said.
2 The previously described or specified; the (person or thing) before mentioned.