Florida. Check.
September. Check!
Good weather?
I dunnow about that! I tend to immediately think "Hot and stupidly humid, with occasional hurricanes for extra excitement!"
You mentioned New Mexico.
The October trip would be ideal for a nature oriented tour of the 4 corners region. The region within the Albuquerque - Santa Fe - Grand Junction - Green River - St. George - Flagstaff - Albuquerque circle has a few large and medium cities that might be of interest, and gobs of stupidly pretty scenery that will be ablaze with fall colors. Canyons, forests, redrock, mountain peaks, the works. Cities to visit might include... Flagstaff is a cool college city that might appeal. Albuquerque is somewhat of a sprawl, but might be worth checking out. Santa Fe is getting kinda big, but still has a hint of small town intimacy. Cedar City is lovely if you can stand the Mormon tilt. (It's about as far removed from the weirdness of Portland as you're gonna get!)
IMO, one of the better combinations of Small Town America and glorious scenery is the Hwy 89 drive from Arizona to Wyoming.
Start at Sedona (fly into Phoenix?) and head north through Flagstaff, Page (after a short side trip to the Grand Canyon), Kanab (numerous AWESOME hikes in the area), Mt. Carmel (Zion NP is 1/2 hour away), Panguitch (Bryce NP), and then up the central valley of Utah, where you'll see dozens of lovely little cities. On to Salt Lake City and Logan. Up Logan Canyon (superb fall colors!) to Bear Lake. On to Afton (see the Elkhorn arch and hike to the Periodic Spring!), Teton National Park and then to the magnificent-beyond-words Yellowstone! Drive back to Salt lake or continue to Bozeman MT to catch the return flight.