I have done the North Rim of Yosemite as early as early May. You will have a bit of snow but it usually is hard enough to walk on, the only problem is that it covers the trail and when in thick forests it is easy to miss the trail. A GPS helps.

I have also done the Pohono Trail early. Again, same with snow, except usually a bit more. IF glacier point is not open just keep going on Panorama trail and come down the Mist Trail. Good loop is start at Wawona tunnel, Pohono Trail to Glacier Point, Panorama to LYV, then down the Mist trail or, go up the Merced to Merced Lake and take the cross-trail to the JMT and come down it, and then down the Mist Trail. You could just stay on the JMT, but the Mist Trail is a lot more scenic.

Yosemite is great this time of year. Lots of good loops from the Valley. And there is a no-reservation backpackers campground that makes the logistics quite easy.

There may be lots of mosquitoes. So prepare for that.

Not sure if you would be interested, but a good 6-8 day trip is to do the entire Lost Coast from Matolle to Hwy 1. I have done it twice, earlier, and it is great if you are into coastal hiking. The only problem that July is getting a bit late and you may be into fog season. You also need to look at tide tables, as there are several spots that you need low tide to get around.