I think ideally you tour should be U-shaped. You start for ex in Vermont in summertime, head down to the southern states for the wintertime and head back up Califronia the next summer.
I have been in North Carolina, Florida, Georgia, New York, Vermont. Just to give you an idea:
August, nice. Not to hot or to cold.
February, nights as cold as -20°C (in the mountains)
July, hot as hell, lots of bugs.
Florida March, days up to 20-25 °C, but nights might easely drop between 5 and 10°C
If you want to visit the Everglades I think you should do this during the winter months. In summertime it is way to hot to come out. (but then again, what am I used to in rainy Belgium...)
I hope this gives you some info. I am sure there are statistics to find on the net about the climate in the states.