[Rain Man]

Okay, how about this?

There are 22 states in the continental U.S. that are west of the Mississippi.

If you look at areas with 10,000 or more people, there are none that start with the letters Q, X, and Z, so you kick those out. You start in Texarkana, so that takes care of T, and now you have 22 letters left and 22 states.

Try this as a starting point, recognizing that you want Amarillo and Denver in the mix.

TX Amarillo A
MO Branson B
OR Coos Bay C
CO Denver D
NV Elko E
AZ Flagstaff F
KS Great Bend G
AR Hot Springs H
IA Iowa City I
WY Jackson J
MT Kalispell K
NE Lincoln L
ID Mountain Home M
LA New Orleans N
OK Oklahoma City O
WA Port Angeles P
MN Rochester R
NM Santa Fe S
CA Ukiah U
UT Vernal V
ND Williston W
SD Yankton Y

As a route, I might suggest:

TX Amarillo A
NM Santa Fe S
CO Denver D
AZ Flagstaff F
UT Vernal V
NV Elko E
CA Ukiah U
OR Coos Bay C
WA Port Angeles P
ID Mountain Home M
MT Kalispell K
WY Jackson J
ND Williston W
SD Yankton Y
MN Rochester R
IA Iowa City I
NE Lincoln L
KS Great Bend G
MO Branson B
AR Hot Springs H
OK Oklahoma City O
LA New Orleans N