If you haven't already, be sure to go to the official National Park Service website for the Grand Canyon, http://www.nps.gov/grca/index.htm. There is a wealth of information there on all the things you need to know about your visit.
I have camped, stayed in a cabin and stayed in a modern motel on the south rim. I have stayed in a cabin on the north rim. All have worked for me, but some day I would like to stay in the original old lodge, El Tovar.
Keep in mind that the south rim is at about 7000 feet of elevation. This can be a problem for some people and altitude sickness can happen. The elevation also affects the temperature and it can be colder than people think AZ should be.
The information below is somewhat hard to get to on their website, but is found if you scroll down on this page -- http://www.nps.gov/grca/planyourvisit/weather-condition.htm..
"By mid-April, winter weather usually begins to break, and although snow is not uncommon in May, warm spells become more frequent. The winter cold gives way to a warming and pleasant spring period with average high temperatures gradually rising from the 50s and 60s (10-21°C) in April through the 70s to 80s (21-32°C) by June along the Rim, and from the 80s (27-32°C) in April to near 105 (41°C) by June along the river. Low temperatures will typically fall below freezing on the Rim in April and May and warm into the 40s (4-9°C) by June, with low temperatures from the 50s (10-15°C) in April to the 70s (21-26°C) by June along the river. Spring is typically breezy to windy with winds occasionally gusting over 40 mph (18 m/s) and dry with little precipitation occurring in May and early June. Due to the very dry airmass typical of the late spring months, late season frosts and freezes are still a possibility, with sub freezing temperatures being recorded as late as July at the North Rim. Snowfall has been reported as late as the middle of June."
Of the 4.5 million visitors each year, 2-3 fall over the edge, so it is possible to get very close to the edges of the canyon, but our daughter who took her 3 kids when they were 14 months, 5 and 9 didn't mention any particular concerns for them on that trip. They stuck to the safe trails, I guess.
The canyon runs east and west. One year when I was there close to Mother's Day, the sun was setting in the west at the same time the full moon was rising in the east. It was magical and mystical. There were people way out on some of the promontories that evening, but I was not one of them. I could see the phenomenon just fine from considerably farther back.
Wherever you stay, enjoy your trip to AZ.