There are 10 Inyo National Forest campgrounds along the June Lake Loop, and they are listed under the Mono Lake Ranger District. I've never camped at any, but I've driven by them, and I think the prettiest location on that road is Silver Lake. Campgrounds on the June Lake Loop are approximately a 1-hour drive from the Tioga Pass entrance of Yosemite. The advantage of staying somewhere along the June Lake Loop is that there will be places to eat; and the tiny cafe at the privately-run Silver Lake Resort is locally known for their homemade breakfasts.
There are several more campgrounds off of CA State Route 120 (called Tioga Road within Yosemite) that lie between Lee Vining and the Tioga Pass entrance to Yosemite, and/or near Mono Lake. So there are quite a few choices for camping in the area, 19 campgrounds in the June Lake/Lee Vining/Tioga Pass region, if I counted correctly. I'm pretty sure that the Tioga Lake campground is the closest one to the Tioga Pass entrance of Yosemite, but none of them are all that far away, really.
For further information see:
On that last page linked above. click on "Campground camping," then scroll down to "Mono Lake Ranger District"
Edited: 6:51 pm, December 01, 2011