I don't know how MPD is layed out (if it's a campus or just some building or what) but yes, you will need a car in Farmington. The weather is generally nice so a motorcycle will work most of the year, but not in the winter since it snows.

I'm not sure what you like in a ciy, but Farmington is small. This means that if you have a long day (which is common during pilot training) that most places will be closed when your day ends. There are a couple of 24 hour places, but it's crappy food that'll make you fat and feel sick. Farmington is also a considerable drive to any sort of metropolitan area, so if you need something even slightly obscure, plan a cross country to Albuquerque or Pheonix or Denver.

I didn't go to MPD, but I have been to Farmington and spent plenty of time in little western cities like it. They have their pros and cons. Things are cheap and you get to know people surprisingly well, but on the other hand, little changes which makes it easy to get into a rut.

And be wary of the strange desert people. Not a lot of them, but the ones there are, be cautious.