Very Large Array
I'm an unabashed geek, so taking a southward route on the way back to Brooklyn from Arizona in the winter of 2014 we decided to stop through the Karl G Janksy Very Large Array, a series of 27 radio antennae used by astronomers to peer very, very deeply into space. Each 82' dish is on one of three 13 mile long tracks and can be reconfigured to a variety of positions, effectively making it up to a 21 mile wide antenna dish. You may also know them from the 1997 film Contact, though many more were digitally added in that flick to give a much denser feel to the field.
It was cold and windy but I couldn't get enough of them. The fact that the array is located at high altitude and pretty geographically distant from pretty much ... anything ... definitely makes it a specific destination, but I can't recommend stopping in enough if you'll be anywhere near the site. It is quiet, peaceful, very impressive, informative and one of those places that restore your faith in the future of mankind.