Isn't it more like about 9 miles round trip from Hodgpodge to Tuolumne Grove and back?
Pretty decent, no?
You can ziggy doo over to Hodgden Mdw... well... right before there and hang a left...
head down to Carlon Area... and hike up to the falls. Very nice little area.
That's only about 7 or 8 though. But worth the effort imo.
Not sure what time this whole campground thing is... but if Tioga is open...
Hodgden is your ticket to a better place... with Yosemite as your Oyster to explore.
Any and all trails on Tioga Rd. are worth exploring.
Have fun