Is Fairbanks your only Alaska destination?
I live in Anchorage part of the year, work on the North Slope part of the year then the lower 48 the rest of the time.
It would be a shame to drive all the way from TX to AK and only see Fairbanks.
WHile the ride from Tok Junction to Fairbanks up the Richardson Hwy os pretty, I think it pales in comparison to heading south on the Richardson. Stop and see half the world from the top of Thompson Pass, pull over in Keystone Canyon for Bridal Falls, lots of eagles in Valdez.
I prefer Fairbanks in the cooler or colder months, better chance of seeing the northern lights. The summer moths are just to hot, but being from TX you'll probably not even notice.
I've driven the ALCAN 4 times now and each time it's different. Only one trip in the summer the rest have been in the fall to take the RV south for the winter.
I can't give you any great stops along the ALCAN other than the normal tourist places. My suggestion is once you are past the tourist places, drive slow and enjoy the scenery. Especially north of BC and all of THe Yukon.
If you like german cooking don't pass up Northern Rookies Lodge at Muncho Lake. Canada Fly In Fishing Vacation - BC Fishing Lodge & Wilderness Adventures- Northern Rockies Lodge
A little pricey but then what isn't on the ALCAN. Not a great CG though, spaces are tight and the power pole is at the front of the site.
The prettiest road/drive in my opinion is the Seward Hwy south of Anchorage. Take it all the way to Seward. In Seward you will find a City RV park right on Resurrection Bay. On you way to Seward you can stop and see Exit Glacier, the Alaska Wildlife Conservation Center, Beluga Point, Cool Inlet with a 30' tide swing, etc... Seward is a nice little town, great food and coffee. You can park at the city CG and walk the whole town.
When you finish in Fairbanks consider coming south on the Parks Hwy. Stop and se Denali, eat breakfast at the road house in Talketna (cinnamon rolls as big as your head). THen if you have time continue south to Anchorage, Seward, Kenai and finally Homer. If not, head east on the Glenn Hwy back over to the ALCAN.
If you make it to Anchorage let me know, if I'm in town dinner is on me.