Grand Canyon to Santa Fe is nearly 500 miles and will take you about 8 hours on the road. In other words, it won't leave you any time left to "spend the day" in Santa Fe. At that pace, I don't even see the point of going there, as you will have at most a couple hours in the evening to "see" it, before doubling back to Albuquerque the next morning.
White Sands to San Antonio is more than 600 miles to San Antonio, and is pushing the limits of how far you can even safely travel in one day. Despite what online mapping programs may tell you, you're going to be on the road for 10-12 hours there, which won't leave time for really any "interesting" stops.