Before school lets out or after school starts.
spring is when you get to see babies...bison, bear, etc. but still pretty cold.
fall weather is cool but not cold but also subject to a freak early snowfall.
but the restaurants and visitor centers close around mid Sept.
but they don't get opened until mid to late May.
:)
so really, you have the last 2 weeks of May or first 2 weeks of Sept.