Out of Mammoth Lakes, there are several trails that lead to good camping locations, too. Garnet Lake to the northwest. Duck Lake to the south.
I "second" these suggestions. You can also do a loop from Lake George to Lake Mary via The Deer Lakes, and Duck Lake. From Lake George hike up to Mammoth Crest, and down to Deer Lakes, and out the other side, and down to Duck Lake. Lots of options for camping along the way. From Duck Lake, hike out toward Lake Mary, but there is an alternative trail that will take you back to Lake George. You could also leave a car at Lake Mary, and drive back to Lake George.
Garnet Lake is (I think) a better option. Depart Agnew Meadows, to Shadow Lake, to Garnet Lake. Many of the PCT hikers will take this option. Stunning. From Garnet Lake you can make a loop by taking the River trail back to Agnew Meadows, or you can go on to Thousand Islands Lake, and hook up to the PCT, and back to Agnew Meadows.
Another option (from Devil's post pile) would be Minaret Lake. Lots of camp sites here. It is possible to continue north to Lake Ediza (but I'm uncertain of the trail conditions), and then loop back via Shadow Lake to Agnew Meadows.