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I just want to bounce this off of people who are familiar with the Canyon, like Al, who can sound in, both for me and anyone else who may be reading.

From looking over trails at the canyon, the basic summary of those that leave from the South Rim and are accessible as day hikes are:
The Hermit Trail, Bright Angel Trail, South Kaibab Trail, Grandview Trail, New Hance Trail, and the Tanner Trail. It looks like the only one that does not reach the River is the Grandview, and the primary ones that are well maintained are the Bright Angel and South Kaibab, the others being in rough shape.

Having day hiked to the river and back on the Bright Angel and South Kaibab, which of the other above mentioned trails offers the best views of the canyon? From GPS plots, it appears they are all about the same and do not climb in canyons as the BA does. My assumption would be that the Hermit trail is not really convenient to access this time of year with the bus requirement and the time consumed with riding it, so it is better to use the trails on the east drive. Keeping in mind that I drive up for the day, prefer to sleep to between 6 to 7 AM, and day light is getting less and less in the evening. Of those, which do some hikers favor the most? That is, if you were to do a next logical step trail, which would it be if you were me?

Also, from looking at the Grandview, the cavern hike might be a nice alternative to going to the river. Is it as easy to find with no GPS as one might like it to be?
Thanks

I was thinking about a lasso along Grandview in the future. I didn't see a route on the site for the trail that runs east/west passed Miners Spring from Grandview to Tonto. Does anyone know much about it?

Based off of the topo maps, I'm looking at the following: down Grandview, west down Cottonwood Creek to Tonto, then to the trail mentioned above and back up Grandview. Could probably shorten it by heading all the way down Grandview to Tonto and going left or right to get back to the trailhead. Recommended? Discouraged? I don't know much about GC.

There is a trail that starts from to top of the mesa and goes off the east side of horseshoe mesa, it will pass the turnoff for Miners Spring, and end down to at the intersection with the Tonto a litle bit west of Hance Creek. From there you can take the Tonto around Horseshoe Mesa to Cottonwood Creek and come back up Cottonwood Creek onto Horseshoe Mesa. I have done all but the Miner's spring part of this loop already, and will pick up this missing piece this Spring.

I've done the trail that goes off the west arm down the north side of Horseshoe Mesa - it isn't that great. Doing the lasso per your original idea may be more enjoyable. However it's pretty long for a dayhike, might be better as an overnight backpack.

The Cottonwood Creek/Miners Spring loop looks to be somewhere around 12-13 miles. Sounds doable as long day, but the climb out would surely be a slow butt-kicker. Perhaps the trail along the west arm with a loop back around Miners Spring, which is somewhere around 10-11 miles, would be better. Especially with Cave Of The Domes.

I'm thinking of doing this, or something else at the Grand Canyon (if the weather/trail conditions permit) for AZ's centennial. This is really the first trail I've considered...

Why not backpack down to H.M. (3 mi.) drop your gear there and do the day hike clock-wise, picking up water @ Miner's in the afternoon for your evening's camp on H.S. Mesa and do the cave in the AM and hike out after that.
No reason, IMO, to rush through ANY hike in the Canyon.

If I did it in a day, I would definitely want to stay longer, but I don't have the gear for an overnight right now.

That photoset makes a solid argument, Jake.