<p>Dartmouth is more competitive in admissions than several schools on your list (look at, say, the SAT statistics in US News and World Report). If you are looking for a safety in the North East, Dartmouth is not a good choice for you, though it is an excellent school in its own right with a very good undergraduate math department.</p>
<p>The distinction between Dartmouth and Harvard, MIT or Princeton in math is really only relevant if you are advanced enough in math that you can, say, start with real analysis in your freshman year and are ready for grad courses (which Dartmouth actually has) by your junior year.</p>