I want to pursue some combination of mathematics, computer science, biology (genetics/neuroscience) and physics and I think computational neuroscience would be an ideal field for me to pursue.
Firstly, do colleges even have that degree of specialization at the undergrad level?
And if they do, which are some reputed programs that I can explore?
You can double major or major in one and minor in the other (e.g., major in neuroscience and minor in CS). Most colleges do not have that level of specialization at the undergrad level, but some will.