Remember, if you do choose Mexico or somewhere outside the US you will need to get a passport, even for a 2 month old.

I would suggest Puerto Rico; you won't need a passport as it's part of the US.

Keep in mind that if might be easier to go to a "walking" destination rather than a "beach" destination. Newborns can't just lounge on the beach soaking up rays, but will fall asleep in a stroller while walking though a museum.