Are you flying or driving? If flying: Katmai, Yellowstone, Grand Teton, Glacier, Hawaii Volcanoes
If driving: Mammoth Cave, Great Smokey Mountains. After those two your options get severely limited due to the length of time it will take to drive. If you only have a week and you have to drive at least two days each way, it no longer becomes fun. At that point I would suggest Gettysburg, PA (might be tough for a 6 year old) or Colonial Williamsburg, even though they aren't National Parks.
Definitely heed the advice given about timing. Being miserable because it's too hot or too cold is not fun. You can't foresee every potential weather event but you probably don't want to be in Death Valley mid-summer or in Katmai in April.