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The European Organization for Nuclear Research, aka CERN, has a wonderful summer school, and provides local support for eight and 12-week schools. Students must fund their own flight, or find external support; no stipend is offered (but all meals, etc. are covered). Read about Badisa Mosesane’s (U-Botswana) experience in 2017.
CERN’s US-based REU program for their summer internships provides a stipend, per diem, and travel for selected students (this might be more appealing to students who need the stipend).
National Center for Atmospheric Research “SIParCS” – is a paid summer internship program for undergrad and grad scholars. Interns receive a stipend plus housing support (this could change from year-to-year, project-to-project). Interns engage with a variety of tasks: most involve programming and statistics, but some would interest a future HPC sysadmin.
National Science Foundation REU site database; search for “high performance computing.”
National Center for Supercomputing Applications (NCSA) Cyberinfrastructure Professional Intern Program (CIP).
XSEDE Empower is for undergrad students at US universities who participate in a three-tiered, progressive internship experience (learner, apprentice, and intern). Students must be matched with a professional mentor who works for an XSEDE institution. Stipends are granted that vary in size depending on the number of hours committed.