High Sierra Topix

I agree with WildHiker re. Meeks Bay and up chain of lakes. You can come out at Bayview as he says or at Eagle Falls. This is a busy highway and its easy to take one car and let one driver hitchhike.

Twin Lakes to Peeler does have some steep climbing as you approach Peeler, but it's moderated by the switchbacks. Peeler is interesting in that it has an outlet on each side. The water flows around a mountain range that is at the same time an island.

Aloha is going to be pretty regardless of whether the water is low. Someone just posted a trip report and there's actually still a lot of ice and snow there, though Rockbound Valley on the other side of Mosquito Pass is dry as a bone. You might do a few yards of XC to Lake Le Conte for a private little campspot, but I don't think there's any shade there. There are all kinds of little tarns around Aloha to find little private retreats if you're willing to do a bit of scrambling.

If you really want to wow visitors with roadside and trailside scenery and get out on easy backpacking this 4th of July, I agree taking them up Tioga Pass Road (HWY 120), and then backpacking from Saddlebag Lake (no quota) or from Agnew Meadow/Minarets area (farther and more complicated) is worth driving beyond your stated four hour parameter. Time permitting, roadside vistas and short hikes along Tioga Road from Tenaya Lake-Tuolumne Meadows area are hard to beat through fresh eyes. Looping back over Sonora Pass (108) would be possible for additional sightseeing and for traffic avoidance if not driving back in the dark (I end up in the dark a lot to hike more).

For future reference, besides Tahoe-Desolation area, I'll add that Lassen Volcanic NP, Mt. Shasta, and some parts of Trinity Alps Wilderness near Weaverville are potentially within 3-4.5 hours and lacking traffic once on I-505 and I-5 from Vacaville. They are not quite Tioga Pass-Yosemite-Minarets through my eyes, but (IMO) as worthwhile as Emigrant or Tahoe area to visit at least once. Plus, they will still have some snow to gaze upon. YMMV. It is great that you already have a permit for a scenic area. Everybody and his mother's uncle goes to Tahoe 4th of July, but lots of people go to other well known mountain spots too.