<p>Graduate admission to both MIT and Stanford is very selective, although how selective depends on the particular department in question – graduate admissions are done by professors in the department to which you’re applying, not a school-wide committee.</p>
<p>Generally speaking, I don’t think it’s wise to choose an undergrad institution based on the idea that you can go to another place you also like for graduate school. In the first place, you may change your mind completely about even attending graduate school. Somewhat more subtly, you should never pick a graduate program based on the overall reputation of the school where it’s housed – graduate studies are very specialized, so you should pick a graduate program based on specific professors with whom you’d like to do your graduate work.</p>