Here's a working map:
Map of Canyon, TX by MapQuest
You said this is a winter trip, so I will assume you're coming from the North. If it were my 10 days.....
Take 37 south and see Palo Dro Canyon, just south of Amarillo. Keep south and work your way down to Big Bend N.P. Drive the blue roads along the Rio Grande. See the little border towns, and be thankful you have what you have. Cut across 90 and spend a night in San Antonio. Call me and I'll buy you some margaritas at Mi Tierra. Head down 37 and see Corpus Christi--a beautiful city! See the Lexington and the Aquarium, and spend the night in Port Aransas--it's empty this time of year, so stay right on the beach. If you're camping, hit the Malaquite SP on the beach. Coming back is a pain--no other way to travel but 37. Catch 281 and take it all the way up the State on your way out. If you want to swing over to Austin, 290 takes you there. Dallas/Ft. Worth, 67 takes you there....It also takes you to 35--the main N/S artery.
Enjoy your trip if you come down. Remember Margaritas at Mi Tierra!