Sorry, just realized you were asking about times to go. I wish I could predict a good time. Weather varies so much up here, it's hard to say. PD is going to be crowded Spring Break, after Memorial Day, and on pretty weekends. It's just a 20 minute drive from Amarillo.
As above, March is the windy month, late May thunderstorm season, and July and August damned hot down in the canyon. Mid June through late August is the "Texas" musical drama, which brings its own crowds.
As I said above, we've started the year wetter and warmer than average, but snow in April is not impossible, though unlikely. Things start to green up slowly after mid March, and the wet winter probably means some nice grass and flowers.
We are at about 3500 altitude and usually low humidity. Nothing but flat plains for 100s of miles any direction, so weather systems blow through often, from any direction. The altitude and humidity means the temps can swing wildly, but nights almost always are nice and cool, even in summer.
I think the little one will enjoy the canyon, but if the weather turns bad, the museum in town is one of the finest regional museums in the country.
