Thanks for all the great responses. Reading all this gets me really excited about going even though it so far away. I originally mentioned the July-September thing, but really that's just because this is my first year out of school and I'm so used to only having vacation time in the summer. Now that I can take it whenever, it seems to make more sense to do it late September - October when it's just as nice and the crowds are less.
Also, never having been to these I was unsure about how much time you really spend in them because I know they vary greatly in size. So for a lot of these, it makes sense to try to visit a couple in one trip? And which would be best to combine in a trip (Teton/Yellowstone, Zion/Bryce, etc.)?Remember it's only my first year working so taking off more than a week at once isn't a great option, so the longer type of trips I'll have to put off until future years.
Any more advice/experience is greatly appreciated.