Unless you love to ski, January is the worst month to visit Colorado. It is colder and darker than the rest of the year. Go to Arizona, it's cooler and the hiking would be good.

October is a great month to visit Texas, and as it's so large and diverse, you could spend your entire month there and not repeat any category of scenery.

Unless you love to ski, January is the worst month to visit Colorado

Even if you do love to ski! I was in Aspen last year and it was 3 degrees below 0 F. Mightly cold.

The plan calls for Dixie and Desert

If you have to go in January and plan to stay a month, I would plan to start in Florida and work my way from Miami north to Orlando, Tampa, and then up to Charleston, west to New Orleans and Cajun Country, then onto Texas and San Antonio/Austin, and then west into the Desert Southwest (Tucson/Phoenix). Finally, work your way west to San Diego and then finish in LA for your flight back home. This route will avoid bad weather for the most part.

In October for a month, I'd plan an Eastern Seaboard tour from Miami north to Charleston, then north to the Smoky Mountains, then onto DC, Baltimore, Philly, NYC, and then up to see fall colors in New England. Then, finish out in Boston for your flight back.

Actually, in October, I'd plan the reverse trip because (a) fall colors are better earlier in the year in New England and (b) weather is better in New England earlier in fall and better in the South later in the fall.

So, for the October itinerary, plan to fly into Boston, and head down to Miami using the cities I listed, but in reverse order.

All of the Northeast is at its best in the fall, but I would second the recommendation to start North and go South, rather than the reverse. If you can stay for Halloween, I would highly recommend that too. I understand the way we celebrate it is very different from anywhere in Europe.
Only children go trick or treating, but the shops are full of neat decorations, some people decorate their homes (often very creatively), there are haunted houses, corn maizes, hay rides, etc. to visit, and many bars and clubs have Halloween parties (with patrons in costume) the weekend before, and often the night of.
January is a more limited month, but much of the south is mild (as my mother says "they have winter, but it ain't much") and much of the country is not too horribly cold. And Florida is lovely in January.

If you end up in the South at the end of October for Halloween, I'd recommend having New Orleans as your place to celebrate Halloween. Halloween in New Orleans is like nowhere else and you'll highly enjoy it.

I don't have much of a suggestion for you as far as January goes, but you HAVEN'T seen the best of America until you've seen the Smoky Mountains in the Fall. October is the best time of the year to visit the Asheville, NC area. There's nothing like the beauty of the mountains when the leaves are changing. We live in the most beautiful place on earth! (or so we like to think) It's chilly here in the winter, but not like the northern states. Don't end your visits to the U.S. without visiting here. Upstate South Carolina, south western North Carolina, and southern Tennessee form a triangle of wonderful landscapes full of wildlife, natural beauty and hiking trails that you will love! It's nothing like Chicago or San Diego - Atlanta and Charlotte would be the closest "bigger cities" and they are both at least 2 hours away. These are smaller cities and towns that are unique and full of southern charm. Do a search of Asheville, NC, Pigeon Forge, TN, Cades Cove........some people might not think it's worth it but if you've never seen it, it will be!