Here are a few more programs to check out. I don’t know if they all offer neuroscience.
https://grad.ucla.edu/admissions/diversity/summer-programs-for-undergraduate-research-spur/
http://www.utsouthwestern.edu/education/graduate-school/programs/non-degree-programs/surf.html
http://www.mayo.edu/mgs/programs/summer-undergraduate-research-fellowship
While I was looking up these links, I found this list which includes some of the above programs:
https://www.aamc.org/members/great/61052/great_summerlinks.html
Good luck with the search! I’m sure that he’ll be accepted to a great program.