Criteria for choosing undergraduate school to prepare for graduate study: "focus on undergrads" & "extensive rigorous curriculum" mutually exclusive? I'm trying to figure out which undergraduate colleges are most conducive to graduate school applications, but it seems to me that (with few notable exceptions) my two main criteria that lead to this sort of success are mutually exclusive. Are there any schools in the U.S. that have both an extensive mathematical curriculum and a focus on their undergraduates?

Schools known for being strong in math (such as MIT, Harvard, and Stanford), seem to be very heavily focused on their graduates, with comparatively less attention payed to their undergrads. I'd like to avoid classes taught be TAs and be able to learn from and get to know my professors, both for the improved learning experience and the improved graduate school recommendations that will inevitably eventually result. Perhaps even more importantly, it seems that research as an undergraduate tends to improve students' chances at graduate schools; thus, colleges that have significant research at the undergraduate level are most appealing.

However, schools with the above desirable criterion tend to be less mathematically rigorous, especially in pure math. I've found a handful of schools that will even keep a math major occupied for a whole four years if they've taken only introductory multi-variable calculus, linear algebra, and differential equations. I don't want to have to sacrifice an education for attention -- I also want to go to a school considered highly for graduate school that has extensive course options.

Is the first criterion a fair voting system and the second a dictator? Is there any intersection of the above specifications? My own rudimentary research suggests a few options, but these hardly make a list even the best students can expect to be comfortable applying to. 

I want to make sure I have the best options for graduate school in the future, both in being a qualified applicant with the opportunity for stellar recommendations and in having learned the extensive mathematics required to give me a head start for future research.
You'll need to decide for yourself which sort of school is the best fit for you educationally (this is a highly personal decision, and a school that's a wonderful fit for one person might drive another crazy).

However, I don't think a focus on undergraduates matters much regarding preparation and admission for graduate school.  Not even in the ways you'd think it should, like getting good letters of recommendation: there are disproportionate numbers of students in top graduate programs who attended institutions nobody would describe as focused on undergraduates, so this is clearly not keeping them from being admitted.  In particular, faculty at universities with strong math programs know what it takes to be admitted to top graduate schools, and they provide what's needed.  You might have to put in some effort to make sure you don't fall through the cracks, and this could be a hardship depending on your personality, but for many people it's not so difficult and in any case it's a valuable life skill to develop.

If you're looking to judge universities by how well they will prepare you for graduate school, the main factor I'd look at is how many students they send to graduate programs you might like to attend.  If the number is large (relative to the size of the undergraduate program, of course), then that's a very good sign.  Clearly they're doing something right, and you'll have the benefits of a strong peer group already as a undergraduate.  If the number is small, then you should worry.