Day 1: Enter the park, stop at Fishing Bridge and walk across looking for wildlife. Turn south and go around the Lake, stopping at West Thumb. Head to Old Faithful, check in at Visitor Center to see if anything interesting is set to go this afternoon and walk to it. I would recommend doing a more thorough tour of the Upper Geyser Basin on day 3.
Day 2: Since this is the day you are doing the cookout, make this your Upper Loop day. Head to Norris then Mammoth. Tour the Upper and Lower terraces and stop at the Visitor Center. The best bathrooms at Mammoth are the new ones near the bus parking lot. Go to Roosevelt, head out in to Lamar Valley if you have time before you need to check in for your ride. Take extreme care driving back to Old Faithful. You will need to go slower than the posted speed limit due to big black slow moving animals who insist on walking down the middle of the road.
Day 3: Make this your geyser day. Start at the VC, do the Ranger walk (830 maybe??) Do the upper geyser basin, then drive north doing the smaller basins, Midway, Firehole Lake Dr., go almost to Madison Jct (or go all the way there if someone needs a bathroom, they have flush toilets). Take the left turn into Firehole Canyon Dr. Return to the main road, pick up Fountain Paint Pots. If you have plenty of time, you might want to continue past Madison to do Gibbon Falls, or drive part way out toward the West Gate. If you do that, turn around at Gneiss Creek Trailhead or continue a little way further to Riverside drive. Do that and then head back toward Madison Jct. The usual suspects (elk and bison) are along this road, you might also see Bald Eagle, trumpeter swan and some have seen otters in the river (I have not!!)
Day 4: Head to Canyon. Stop at Visitor Center. After that I would head down into Hayden Valley looking for wildlife, do Mud Volcano, Fishing Bridge again, go back north and do LeHardy Rapids to scan for wildlife, then when you get to the South Rim, do that side. If time permits, start on the North rim, then get to the amphitheater by 430. Again be VERY careful driving down to Grant and try to get there before dark.
Day 5: Wave bye-bye to Yellowstone!