So, I'm going to be in the Grand Canyon this June (I know, hot, right?). A rim to rim would be fun, but it seems logistically easier to stay on the South Rim. I'm thinking about taking the early morning shuttle out to Hermit, then down to Tonto, stay the night at Indian Garden (20.7), then either straight back or Phantom Ranch and back up the next day.

Does anyone have any personal experience to offer with that section of Tonto? Any suggestions/things to change?

The stretch of the Tonto between Hermit and Bright Angel is very nice. Well established trail and for the most part easy walking, without being a massive trench like the main corridor trails.

June is certainly hot, but very doable. Plan on hiking early and late, and holing up in a side canyon during the heat of the day. Monument Creek in particular is cool to explore (and soak in the cool water).

I'd avoid camping in Indian Gardens, too crowded. Horn or Cedar Creeks are very nice sites.

The side trip out to Powell Point is highly, highly recommended.

The Tonto section between Bright Angel and North Kaibab is also very nice, going up the Kaibab has better views, too.

look for the big number "7"
and dont drink from Horn creek.
temps will prolly be 95-100.
here is a grip of info, and a noaa weather forecast link: http://hikearizona.com/decoder.php?ZTN=1448
have a blast!

any advice on whether I should do the Tonto from Hermit to Bright Angel or the Escalante on the other side? I"m having a hard time trying to decide between the two, and I need to apply for my permits soon.

The Escalante is several orders of magnitude harder. If this is your first trip to the canyon, especially in June, the Esca is a not a good choice.

An alternate, with comparable distance but a bit harder, would be going down Grandview and up North Kaibab. Beware Cremation!

Ok, I may save the escalante trip for later then. Maybe, it looks pretty enticing.

I'm hesitant to do any north kaibab stuff because of car drop logistics, unless you have any good/cheap advice for that.

It seems like something along the western tonto will be the easiest to plan and pull off. Anything you can think of that may be a better first time GC trip?

I meant South Kaibab, not North.

Does anyone have any experience with the "walk to" tent only campsites in Mather Campground? I was going to try and get a reservation for the night before my backcountry permit, but just saw they were first come first serve. In mid June, do those usually fill up really fast? Or will I probably be able to get one? Thanks.

I stayed in the Mather campground walk-in site once in April. For a backpacker site it is tiny, just a regular car camping site that you are expected to share with a load of people. Luckily I was the only person there.
When I checked in at the campground office they asked if i had a car, when I answered in the negative they said "Good, because people ask us all the time if they can camp in that site but we can only give it to you if you don't have a car to park."
So I guess that's the rule and not that many people come to the Grand Canyon without a car.

Oh, how did you get there without a car? I'll be driving a rental car. I was under the impression that you could leave your car in the parking lot and "walk to" the site? Is there a parking lot to leave the car in?

I shared a ride with a fellow hiker to the Grand Canyon. He stayed in a hotel, I camped at the walk-in site.
The walk-in sites do not have parking of any kind. However, you might want to check with the back country office if you could park over there for the night (and also for the days you backpacking.) There is a shuttle system in the park that will take you from the campground to the backcountry office (and many other places.)