I always suggest Houston, but there's not THAT many outdoor things to do...just amusement and indoor based activities.
New England - NYC, historic trails in Philly and Boston and all kinds of Revolutionary War stuff, Lexington, Concord, Cape Cod, the Mayflower II, the rock and the plantation in Plymouth, Hyannis, Martha's Vineyard, Nantucket, fresh lobster in Maine, bed and breakfast in Vermont. The weather and colors should be AWESOME in October if not on the chilly side.
New Orleans - one huge party but very family friendly and very cultural and historical, good cajun eating - oysters, mufalatas, gumbo, biengets, French Quarter, French Market, eating in the warehouse district, WWII Museum (best ever!), City Park, Aquarium, Audobon Zoo, Audobon Park, carriage ride around Jackson Square, riverwalk, shopping on Magazine street...
Take a cruise, or fly to an all inclusive resort in Mexico (either side). Lots of white sandy beaches, crystal blue water, zip lining over clear waters, cliff climbing and diving, sailboat rides, catamaran rides, lots of snorkeling in open water or caves...
If you are looking for outdoor adventure, rock climbing in Colorado. They have 5K, 9K and 15K climbs. There are also plenty of family friendly climbs with easy inclines. There's also ziplining, hiking, rafting, camping and fishing. Just beware of bobcats.