There are several hospital cafeterias within walking distance of the library, and a small cafe in the University of Texas Medical School building across the courtyard. In addition, the John P. McGovern Texas Medical Center Commons (also within walking distance) has a number of quality restaurants and a Starbucks.
The library has a small vending area on the street level, where tables and chairs and a small microwave are also provided for your convenience.
A library employee would be glad to provide you with directions and/or a map when you visit.