Grizzly RV park in West Yellowstone is two blocks from YNP's west gate. And the Virginian in Jackson is less than 5 miles from the south entrance to the Tetons. Both Grizzly and the Virginian are FHU parks. And they're in towns with grocery stores at competitive prices.
No matter where you camp, you'll do a lot of driving. One lap of the grand loop in YNP is about 140 miles. And the drive from the Virginian in Jackson, WY. to the south entrance to YNP is 57 miles. And they are slow miles. But its worth it.
And if you miss something, don't worry - you'll be back. My first visit was with my parents in 1952. Again with college buddies in 1967 and three more times since then. And I'm itching to go again.