We originally thought about hiking from the rim down to the river and back, but the park service issues dire warnings not to do that as a day trip, and backpacking down five thousand feet to face a climb the same distance the following day seemed like a bad idea for two people with occasional knee problems who don't backpack regularly. (I still would like to try it some day, but I'd want to condition our knees by training with weighted packs first. I've injured knees on backpacking trips before.)
There's a lodge at the bottom of the canyon, Phantom Ranch, which allows staying overnight without needing to pack anything in and out, but it turns out to need reservations two years in advance. So that was out.
But it turns out there's an easier way to get to the river and the inner gorge if you have a vehicle you don't mind taking on dirt roads. The Hualapai indian reservation boasts a dirt road which follows Peach Springs Canyon from the town of Peach Springs to the river. Since it's Hualapai land, you need a permit, which you can get for a very reasonable price in Peach Springs at the lodge there. (The lodge looks pretty nice: they have a hotel and restaurant, and might have been a nice place to stay if we'd known.) Then just head down the road, permit in hand (and yes, they do check, or at least someone was checking at the river when we were there) and enjoy the scenery for a while.
It's not a bad road. We have a RAV4, but we saw one passenger car on the road while we were there, and they didn't have horrified expressions. There are some sandy stretches, and some stream crossings (not very deep in October, but I bet they're more challenging in wetter seasons) but nothing that requires serious ground clearance or traction. The views are lovely, especially as you get farther down the road, closer to the river. And the important thing: at least half of the way is in the Schist, so we got lots of up-close looks at this ancient rock.
What's the metal teepee near the top of the road? We never figured it out, but it's interesting.
The bottom has a few beaches which are used mostly for landing and launching river rafts. Rafters coming down through the canyon sometimes use this beach as a take-out, and the Hualapai run calmer-water trips starting at Diamond Creek beach and running down to the top of Lake Mead (the rafts are motorized, for the lake portion of the trip). We saw several raft trailers coming back along the road empty, so they must have launched some rafts; there were two empty ones there when we were there. Dave remarked that the Hualapai are missing an opportunity: Peach Springs road would make an excellent mountain bike run, mostly downhill, very scenic, and the raft transporters that currently come back empty could provide bike transportation back up to the town. Imagine mountain biking to the Colorado River at the bottom of the Grand Canyon. I bet they'd find customers.
Diamond Creek beach sits in Lower Granite Gorge, and the gorge at this point is indeed mostly granite, not schist, on the south side. We hiked upstream for a while, scrambling over broken granite boulders (there isn't much of a trail), and trying to figure out whether the rock on the other side was schist or volcanic (there are a number of basalt flows into the lower Grand Canyon, such as the one at Lava Falls which dammed the river for a while and created the most fearsome rapid in the canyon). We never convinced ourselves either way (though the rock farther up Peach Springs canyon is definitely the schist, with granite intrusions).
We hiked a little way downstream, but that's harder: there's an undercut almost immediately, so you can't really go very far, at least not without going for a swim, which wasn't in our agenda.
We hadn't gotten any close-ups of the schist on the way down, thinking we'd have a chance at the bottom, so we made lots of photo stops on the way back up. I was just finishing taking macro shots of the schist when I slipped on the talus and fall hard on my hand, which immediately started to swell up like a balloon. Dave offered his Camelback (his zips open wide so it's easy to stick a hand inside) for ice-pack purposes, and I iced it all the way back to Peach Springs, which seemed to do the trick: it was much better the next day (which is when I'm typing this report).