Last week I also hiked South Fork, which is slightly easier than Vivian due to less elevation gain. Until a major wildfire six years ago it was pleasantly shaded. It still has some early morning and late afternoon shade due to being on the north side.
It has a particularly nice area, South Fork Meadows, which nearly always has a good flow of water and an abundance of wildflowers. You can do a loop from the meadows, through Dollar Lake one way and Dry Lake the other. There are a few campgrounds, not all of which have water. This is a very dry year, so water sources higher up might be unreliable in another month or two (everywhere on the mountain).
Vivian is a slightly shorter drive which probably contributes to its popularity. After the fires this past summer it’s the only open trail that runs through unburned forest. It has some meadow areas along Vivian Creek and High Creek which are very nice in wetter years.
You can also go up via Fish Creek, on the eastern side of the mountain. This has the least elevation gain, but a long drive on a somewhat rutted dirt road. There are a pair of campsites along the way.