Late October is a fabulous time to visit DC with a side trip to Williamsburg, VA (Busch Gardens is open on the weekends and is gorgeous that time of year) or to Shenandoah Valley(Skyline Drive - you can stay in an old style Lodge complete with no TVs).
When we take our kids places we like to do a few days in one spot and then move somewhere else that offers something different. So city with country/National Park. After a few days in museums our kids get sick of it so having some outdoor time is a good balance for us.
My husband and I did a trip to Plymouth and Boston last Fall after being there with our kids two summer's before. There is so much history and you can mix in fun stuff like the Science Museum and Aquarium. When we took the kids we flew in to Manchester, NH, drove to the White Mountains area of NH and explored the National Forest, streams, hiked, etc. Then we drove to Montreal and stayed a few days there - so cool that people speak French!!!, then drove through Vermont on the way to Boston where we stayed for a few days. My kids loved this trip!!!
If you were going in early September I would recommend an Alaskan cruise. There are less kids that time of year, but we took our kids when they were 5 and 8 on the last sailing of the season, it was inexpensive and they loved every minute of it. Round trip out of Seattle lets you see a bit of the Pacific NW.
We did Seattle again this past summer for a longer period of time and it was fun! We also went to Mt. Rainer - so beautiful and the girls loved the snow (in the summer) Late October, the roads might be closed.
We have also taken our kids on Thanksgiving vacation to Gatlinburg. So fun! We stopped in Atlanta on the way up, then stopped at all kinds of parks on the way to Tennessee. On the way back we stayed a night in Savannah, GA. Gives them a glimpse of all different places they might want to go back and visit when they are older and able to travel on their own.
On our wish list for family vacations is flying to Anchorage and doing an Alaskan land tour (Denali, Kenai peninsula). Oregon coast and parks in the East part of the state. San Francisco and then drive out the National Parks. Denver followed by the YMCA family cabins in Estes Park - late Oct there might be enough snow to ski, if not the YMCA family cabins offer daily activities and cabins where you can cook your own meals, there is also the Rocky Mountain National park there. (Geez, we really like the National Parks!)
I hope that helps. Let me know if you have any specific questions.