The perfect trip for a first time Canadian would be the end of October for about 1-2 weeks. Don't come in the Summer, you'll melt.
Spring would be okay, but still can get a little funky.
Fly into DFW and go to Fort Worth for the most Texan big city. Dallas sucks...sort of, I'm required to say that as a Houstonian.
Head to Austin to watch Formula 1 and hang out with hipsters at the live music capital of the world.
Then on to San Antonio for proper Tex-Mex experience.
Houston could be on the list for days of the best fattening restaurants you've ever had. But really, with a first trip, you'd want to go West. Houston would add too much time. Its best to add for a trip to New Orleans.
San Antonio out to Fredericksburg and the wine country. There be Germans and beer...
And Lost Maples park will be changing colors near then:
Then keep going into the desert all the way to Big Bend.
It gets pretty empty out there
Since you'd be here in November with this itinerary you could overlap the Terlingua Chili fest where 10,000s descend on to an awesome ghost town for a chili cook off
Out West you'll do the McDonald Observatory...
Hit up Hipster Mecca in Marfa
And stop in Alpine
But you won't really hit your destination until Big Bend....
It'll be too cold for swimming, but it'll be amazing for hiking without dying during the day...