Cognitive Science can be a nice major for a possible premed, because it can allow you to get your feet wet in other fields like computer science, without requiring a heavy CS commitment up-front that can make it harder to be a successful premed.
Some folks up-thread are equating CogSci with Neuroscience; neuroscience is more specialized and lab-science oriented, while CogSci is more interdisciplinary. Neuroscience is one component within CogSci, which can be relatively emphasized or de-emphasized depending on the school/program and on the student’s preferences.
In terms of providing alternate paths to employability, it really depends on your coursework. CogSci students with a strong foundation in programming can get software jobs; students who gain research and/or internship experience in user experience design can launch into that field; some who emphasize CS+linguistics can specialize in areas like natural language processing.
As a rule, I think it’s better to major in CogSci at a school that has an actual CogSci department and a core of courses offered by that department, rather than at schools where there is a CogSci major that is cobbled together from courses offered by various departments, but has no departmental home of its own. This isn’t a black-and-white issue, but on the whole a departmental home, with faculty and research under the CogSci banner, tends to lead to a richer experience and better mentoring opportunities. Whether you get priority to register for the classes you need is kind of a separate issue that isn’t necessarily a problem, but can be a problem for CS classes at some schools where those are impacted. (For example, one of my kids majored in CogSci at Rice and didn’t have any trouble getting into classes, but did feel that the CogSci students weren’t anybody’s first priority in terms of advising and mentoring. There is value in having a departmental “home.”)
Schools with robust CogSci departments and a strong emphasis on the computational component include UC San Diego, Carnegie Mellon, RPI, and Vassar. At the Claremont Colleges, CogSci is closely affiliated with Linguistics, but one can choose a more CS-heavy track as well. Schools where CogSci tends to be more neuroscienc-y include URochester, Carleton, and WashU. Schools where it’s more of an enhanced psych degree include Occidental and Tufts. There’s flexibility to tweak your own emphasis at any of these schools, but I wouldn’t suggest schools like CMU and RPI to anyone who’s computation-averse!
If you see Vassar and CWRU as reaches, Beloit might be a good target - they have a nice, balanced CogSci major with robust offerings in several areas of concentration, and strong premed coursework and advising as well. (Also generous merit and need-based aid.) Cognitive Science Major & Minor Requirements at Beloit College
Northeastern doesn’t have a CogSci degree per se, but their combined majors can work well if you’re interested in the computational side and one other particular emphasis, such as CS+behavioral neuroscience, CS+linguistics, Data Science + behavioral neuroscience, Data Science + linguistics. Also, based on your interest in doing something computational within the health field specifically, Data Science + Health Science could be a great combined major: Data Science and Health Science, BS < Northeastern University
Programs like Data Analytics with a biological sciences emphasis, i.e at Denison or at Ohio State, could give you the kind of opportunities you want as well.
The downside of an undergrad CogSci major is that it can end up being “a mile wide and an inch deep” - it’s up to the student to choose depth in their areas of greatest interest. This can be a positive, though, for a student who wants to keep a number of options open and pivot toward a specialization later in their college career.