where to hike arround mid october ?

Zion, other southern Utah areas area good in October and very different from your Alps. I did it last October and loved it.

Ozark Highlands Trail or Ouachita Trail, both in Arkansas.

You might also consider the unconventional California Coastal Trail. You'll encounter day hikers, but also solitude depending on where you start and finish. The weather is usually nice in the fall (65/35*F high/low) with some rain possible. The CCT passes through some of the most beautiful coastline California has to offer, the northern sections especially.

Utah is the most stunning place in the US to hike, in my opinion. Mid-October is the perfect time to go there, as the terrible summer heat has gone.

I am not sure there are any long/unbroken 100-200 mile trails there, and even if there are, I'm not certain they'd traverse through the very best sections.

Get a permit (as soon as possible!) for a 4-5 trek through Grand Canyon National Park. Your itinerary would be: Fly into Las Vegas (cheap to fly there and cheap to rent a car); drive to Grand Canyon; hike GC. Then drive through Utah and hike there before looping back to Las Vegas. There are too many fantastic options to name in southern Utah: Grand Gulch, Paria/Buckskin Gulch, Escalante River, and several national parks including Canyonlands, Capitol Reef, Zion, and others, all perfect for backpacking in mid-October.

How much time do you have?

– Elizabeth