It takes almost a half day to a full day of driving to get anywhere in the state. Many visitor sights are in remote areas and take several hours of driving to get to. The Grand Canyon is about 4 hours from Phoenix. At least one night is recommended while at the Grand Canyon since it is a very large park. It isn't just one viewpoint that you go see. You can't see anything (essentially) from your car. By that I mean that you aren't taking in the vistas while you are driving the couple of hours that it takes to drive through the park. You need to find parking at the overlooks, walk to the edge, look down, return to your car, and off to the next vista. It all takes much more time than you can imagine and will make more sense once you are there.
There isn't anything else around the GCNP for a couple of hours. When I say hours, I mean the next towns are a couple hours away not just that there aren't any tourist sights.
If you only have a day, you don't have time for even the Grand Canyon. Where are you coming from? If you are arriving in Phoenix, you only have time for Phoenix. If you have 2 days, you can do a day trip to Sedona.
You will need a car. There isn't really anything in the way of trains/public transportation.