There are several places to visit which are all pretty distant from each other.
South Rim - Ninety percent of all visitors to the Grand Canyon come here so if you are looking for solitude, this is not the place to come. The El Tovar Hotel, right on the rim is the historic hotel to stay in. From there you can hike along the rim of the canyon in either direction.
North Rim - Since its at a higher elevation than the South Rim the season runs only about six months long as snow closes the park typically until late spring. There's a nice lodge, cabins and some campsites right on the rim with great viewpoints nearby, otherwise there are no hotels nearby. You need to book a room here well in advance as you want to spend at least a night here as it's a long drive to get here from most places in the area. Also worthwhile is the 45 minute drive to Point Imperial and Point Royal.
Tuweep - A remote section of the North Rim of the Grand Canyon accessible via a 60 mile long gravel road. There are no services, just ten campsites. The most dramatic views of the canyon are seen here.
Stop by the visitor center at Pipe Spring National Monument to pick up permits if you are planning on camping here.
Or apply for a backcountry camping permit in advance (recommended as there are only 10 campsites).
Also see my blog post.
Havasupai Falls - Beautiful turquoise waterfalls on the western edge of the park. To reach them requires an 8 mile hike each way. There are campsites and basic rooms near the falls. Another option is to take a 5 minute helicopter ride down to the falls.