The first thing you have to decide about the Grand Canyon is which portion you want to visit:
If you go to the South Rim, you're going to the most often visited portion. It's a national park. It houses numerous hotels, restaurants and other businesses. If you visit during the summer, it's so crowded that you're not allowed to bring in your car; you must park and ride their bus. I don't know whether this is true in May or not, but you should find out.
There's a train trip that provides you with transportation from Williams (?) into the South Rim, and it comes from that general direction. I believe people really like it, though I haven't done it myself. If I had only one day, I think this would be a good choice.
The North Rim is a great choice for visiting the Grand Canyon, though fewer people visit this portion. It's also a national park, though it's closed during the winter months because the roads are too muddy and inaccessible. Instead of multiple businesses and hotels, this portion is much smaller: The housing is made up of a couple hundred little cabins that look like they're made from Lincoln Logs. The Grand Canyon Lodge is the star of the North Rim, though it doesn't contain any hotel rooms. Every night people gather on the massive balcony to watch the sun go down, while the staff builds a massive fire (welcome even in July) in a fireplace so big I could walk into it, and waiters serve drinks. They have a couple restaurants and lots of peace and quiet. The North Rim has an evening cookout with music and entertainment. The big reason to visit the North Rim is that so few people do it; it's much less crowded than the over-populated South Rim. It's also about 10 degrees cooler at all times.
At either location, do check into the Ranger-led programs. We've always found them to be very high quality, and they're free.
If you do want to get a hotel reservation inside the parks, you should do it now. When we went, I intended to make my reservations a year ahead of time, as soon as they opened . . . but I let time slip up on me, and I did it 50 weeks ahead. I got the LAST two-bedroom cabin for our timeslot. Admittedly, we visited the week of July 4th, so it was a popular time, but the point is still valid. Oh, this probably doesn't help you in any way, but they really did July 4th up right: They had a small parade, which evolved into a massive water fight. They set out huge trash cans full of water, and they provided the kids with large water guns. For my girls, it was one of the highlights of a 3-week western trip. It's also the only parade I've ever seen where the participants threw granola bars to the viewers!
Yet another choice is to visit the Western Rim, which is owned by the Havasupai Indians. You may've heard of the Sky Rim, which allows you to walk out over the canyon on essentially a glass walkway. This is in the Western portion. They don't have hotels, etc. at the top of this area, but they do have a hotel and a canyon at the bottom of this canyon; apparently it's quite lush in this portion of the canyon, and they have swimming areas and waterfalls. I really want to visit this area one day.