How much does a student's choice of university matter in terms of finding a job after graduation?
Why indeed. This is a question I get asked fairly often, usually from disbelieving fellow technical majors at other institutions. So let's have the whole long story...
I thought about going to art school (specifically, RISD) instead of a traditional university. I ruled this out because my parents wouldn't have been very happy (of course); my only funding option would have been going into teaching and eventually education policy (which looking back doesn't seem like such a bad idea - but at 17 with no teaching experience yet I didn't know).
Most crucially, I didn't want to just study art. I knew it was something I could perfect on my own (at least, the kind of art I was interested in making at the time) and I also didn't want to stop learning about other things. I thought there was a risk I would be intellectually bored.*
I could have gone to university in the UK: I'd applied to programmes in CS and Business as well as straight-up CS. Once I received acceptances from schools in the US, however, it was to me clear that I would prefer to be studying under the liberal arts system that you get with colleges there. The reasoning was the same. I didn't want to just study CS. In particular, I wanted to try out things I hadn't done before (mostly in the social sciences and humanities) and Yale really seemed like the best place, out of the schools I was accepted to, for doing that.
I definitely was hesitant because Yale is not by any stretch known as a "CS school" - its reputation is more geared towards the humanities. But this ended up also being the reason I came here, and I'm very glad I made that choice. I don't know where else I would have had the opportunity to, for instance, casually check 800-year-old books out of the library (Cambridge and Oxford, maybe, but I didn't get into those). I haven't learnt as much in terms of "practical skills", but (being pretty academically minded and definitely an idealist) I would argue that teaching Node.js or whatever hot new technology is out there is not the purpose of a computer science education. My use of Node.js as an example there probably demonstrates this point already. It would be nice, of course, and there are often times I wish I had learned more things along those lines - when I have ideas for apps and so on - but to me that isn't the reason I paid a lot of money to go to university.
But I imagine this isn't what you're that interested in; let's talk about cold hard cash. It's an awful answer, but yes, it matters quite a lot in the US within certain industries which university you attended. I will say that CS jobs, if by CS jobs you mean those in the current tech industry, appear to be one of the more level and accessible playing fields, particularly if you are 'technical talent' (programmer, data scientist etc.) You don't even need a degree or any formal schooling to be a programmer, really, and that's probably one of the things this industry prides itself on the most.
But you're at MIT, so don't worry.
* Now of course I have a more optimistic view of things. Intellectual excitement is something you can generate for yourself; learning isn't constrained to the university campus. That said, of course to an extent your university environment will have an influence on how easy it is to do so; it's much easier to attend interesting talks about the security risks posed by HDD needles or Chinese manuscript studies, particularly academic topics in the humanities which really don't exist much outside the ivory tower.