Southwest destinations on the cheap is key. Oct 16-21. Kids 12/9/4. We have done East Tenn and N Carolina mountain towns the last couple years via ATL. Just to head to mountains for cooler weather, see some color change, and apple picking. Considering trying somewhere else this year, but will be going via Southwest and driving an hour or two. A couple I'm looking at that have cheap deals right now but open to suggestions:

Denver
Albuquerque
Portland ME (drive to Acadia NP)

Highly suggest Acadia that time of year.

Another possibility is White Mt NP in New Hampshire. Easy drive from Boston which has cheap SW flights

Portland, OR.

I'll take our fall over the east coast any day. The Gorge is firing with maples. Higher terrain has snow and larches. Hood River has apples, pears and pumpkins. Literal Halloween Town is here.

FWIW, I would suggest flying into Boston and taking Amtrak up to Portland. About a 3 hour trip and a pretty cool train ride. We did a coastal cruise two years ago in Maine. Very neat area. Good luck with whatever you do.

Beautiful time of year at Crystal Beach, TX (Galveston). I have a home there, 3rd row, for about $1400 TOTAL for your dates. Hobby or IAH. I book direct.
airbnb.com/h/seahorse-ranch-crystal-beach-tx