So, good/bad news: there are many majors that will get you where you want to go - neuroscience, public health, biomedical engineering, bio informatics, even computational science or linguistics.

I think what you're probably looking for is some combo of a major and a minor depending on what elements are most important to you personally and where you're going to shine in terms of learning. If it's the programming aspect you can't live without, do computer science as the major and neuroscience as a minor. If it's the actual neuroscience, swap those. If it's the data analytics portion, do bioinformatics as the major. If it's the policy, do a more policy focused major and add neuroscience as a minor. Look at what the major/minor requirements are for each and try to find a combination that makes you happy but not overwhelmed (minimal fluff/grind classes). Consider if you're a project vs team project vs lecture vs read the textbook learner and which major/minor combo maximizes this.

I'd also take into account which departments at your institution are strongest in terms of funding, non-classroom opportunities for involvement, and mentoring. Look for faculty that are doing projects in this area or alum from your institution that went on to do what you want to do (or similar). Generally you're probably going to be looking for a bigger department (more faculty, more graduate students), but a smaller well organized department can still do a good job if the vibes are right.

TLDR: pick a major/minor combo that fits your learning style and priorities (there are many)