Good Luck.
Welcome to your National Forest.
There aren't many around Groveland. You could go to the
Groveland Ranger Station (located a ways east of Groveland) and
ask there. But they probably won't know much really.
They will probably just say The Emigrant. Dunno.
Ok, I asked about North Mountain once and they just shrugged.
Here's the map of Stanislaus:
http://www.fs.fed.us/r5/forestvisitormaps/stanislaus/
You can go to Stanislaus and click on Recreation and follow it
to Hiking in the 120 corridor. However most of those trails
are off of Cherry Lake Road... and some (or at least North Mtn)
you won't find unless you are gung ho to get there.
Preston Falls is nice but it may be too short for what you want.
http://fs.usda.gov/stanislaus
Sorry, I don't think there's really much super close to Groveland.
Best to just head straight to Yosemite area.
If you do find something not in Yosemite or out of Cherry Lake please
post your findings.
Thanks
Have fun