@REI-JohnJ. I try to go March or April, better sleeping temps, better possibility to get a permit, just as much a factor, getting a room at Bright Angel Lodge.
This year's trip is first week in May because I decided very late to go again (love planning and taking friends who've never been)
Here's my typical trip:
1. get the permit. I ask for certain dates, then just pencil in "any consecutive dates" as the alternative. Helps if you and your friends are flexible that way.
2. When you get the email from the backcountry office, IMMEDIATELY get your reservations at Bright Angel (@$90) and reservations for a steak dinner at Phantom Ranch.
3. My corridor trip is:
a. night #1 BA trail head to Indian Garden (4.5 miles), with a side trip to plateau point after getting the tents up. pro tip: head to plateau point at night to take sky photos or just lay on your back with a star app and wonder at the stars for a while. For my friends, this is a lifetime memory. (they say) watch out for scorpions starting in May.
b. night #2 Indian Garden to Bright Angel campground 4.5 miles, BA trail, devil's corkscrew, picnic along Colorado River, at the beach. When you find a campsite and get set up, wonder over to Phantom Ranch and get an ice cold beer or two and snacks. After dinner, take a loop hike across the black bridge over to the silver bridge and return.
c. night #3 BA campground to Cottonwood. Side trip to Rainbow Falls. pro tip: there is a path that goes up and behind the top of the giant mossy rock outcrop where the falls splash for magnificent photos. Try to get to CW early because if you're setting up more than 4 tents, you need to get one of the sites that can handle six tents. (not the group site)
d. night #4 CW back to BA campground. More ice cold beer and the 6pm Steak dinner at Phantom Ranch. This is when you buy your souvenirs from phantom ranch.
e. night #5 BA campground back to Indian Garden. IG campground has a little building tucked away that has books! Lots of books also on the flora and fauna and history of the park. A fantastic way to pass time waiting for dinner.
f. last day, try to hit the trail by 0530 or 0600, coolest time of the morning, for your maximum exertion so far, try to walk slow and steady and you will eventually pass those that were just going to run up that trail! Walk at a pace where you don't have breath rear hard.
Victory breakfast at bright angel lodge. Victory dinner at El Tovar (good to get a reservation)
ps: BA gift shop has canister fuel and there is a giant kind of outfitter store/market in the park. But no gas station.
the end. sorry about the book
ps - When we saw the REI group, we couldn't get a reservation at IG and had to camp the first night at BA, so we took the unbelievably beautiful S. Kaibab trail, BUT it was our first major downhill of the season and is an A** KICKER on the thighs, 2 miles shorter than BA trail, but an unrelenting downhill.