Based on your schedule, you really only have one full day available on the Thursday, right? And that will be after a tough hike up on the Wednesday. If it’s your first time, I’d just plan to take another relaxed day on the rim of the canyon. The Grand Canyon is so spectacular that it’s far more deserving of your time, I think - it vastly outshines anything within 1000 miles, let alone a few hours drive.
The Rim temperature will be much more comfortable than Phantom Ranch. You can take some gentle walks along the rim trails to recover from your exertions the day before. The Hermit Road has a tourist bus (and no cars allowed) and many great view points, you can hop on and hop off with the option to walk parts of it. Or hire bikes. It’s less crowded than the central Village area. The geology museum is worth visiting, it’s small but it’s one of the best viewpoints anywhere in the canyon.
If you can’t get Rim accommodation for Thursday night, Flagstaff is only just over an hour away. It’s a pleasant little town, and the closest place with a good selection of restaurants and facilities (there’s nothing much in Tusayan). And, of course, you will get much better accommodation for your money, as you’re not paying for the location.
Between Phoenix and the GC you could stop in Sedona, it’s a nice enough spot with some hiking and decent restaurants. But it’s not remotely comparable to the GC, and it will be crowded and expensive in August.
I think Monument Valley is the closest other big attraction, but it’s too far to drive on your schedule, and the drive to get there is pretty dull.