We did this circular hike in one day, started very early in the morning. We parked the car at the Bright Angel Lodge and took an early shuttle express bus to the South Kaibab Trail head.
The South Rim is open year-round (except for road closures during extreme winter weather, which is rare). The best time to hike the trail is spring or fall, but it also depends on what you are looking for:
March, April, May (spring): Spring weather can be unpredictable but usually temperatures are mild without a lot of rain. However, March is prone to late season snowstorms. Spring is great if you want to avoid the hot and uncomfortable summer heat. It’s also not heavily crowded. There are wildflowers blooming during this season. In some years it can be a gorgeous with lots of blooms.
June, July, August (summer): We do not recommend summer as an ideal visiting time: These are the most popular months with heavy crowds. Although the temperatures are more pleasant than the extreme inner Canyon heat it’s still very hot and midday temperatures can make hiking unbearable. Afternoon rain showers or thunderstorms are common in the summer. Especially from from July through mid-September. Always bring rain gear.
September, October, November (autumn): September after Labor Day is the perfect month for hiking the trail: Less crowds and very pleasant temperatures. However, keep in mind that until mid-September those summer thunderstorms can still occur. Fall weather is also the most unpredictable: Bring rain gear. October and November are still great, although temperatures drop in November: 27 - 52° F (-3 - 11° C)
December, January, February (winter): It’s colder with daily highs in the 40s. Extreme weather with snow storms and and icy trails is possible. However, in the winter you’ll almost find solitude with minimal crowds and reduced rates. It’s a great time if you don’t mind the cooler climate.
Avoiding the Crowds
Summer months bring the most crowds. If you visit in the summer start your hike very early in the morning to beat massive crowds as well as the heat. It can also get crowded in spring and fall during holidays and on weekends. Try to avoid weekends in general. Some great tips from the official NPS website to dodge the crowds: South Rim Crowding: South Rim - A Survival Guide
Please check the monthly weather with temperatures and precipation here: South Rim Monthly Averages. Remember to bring rain gear, regardless of the season.