You can easily do a loop out of Jackson!
Here’s what I would suggest for 9 nights:
Day 1: Arrive Jackson. Do a quick grocery shop and overnight in either Jackson or Grand Tetons to give yourselves some flex on case of travel delays.
Day 2: Head to OF. I, also, like the Lodge cabins but even 2 cabins might not work for your group. Be sure to book directly with the official concessioner, Xanterra, at www.yellowstonenationalparklodges.com
Don’t just google “Yellowstone lodging”or you will get a 3rd party who charges 10% for booking and has terrible cancellation policies.
Day 3: spend today in the Upper Basin trying to see some of the big showy predictable geysers. My favs are Grand and Riverside. Overnight OF
Day 4: Head to the North entrance or Canyon. I often stay in Gardiner at Yellowstone River Motel. It’s family owned, older but clean. Get rooms in the new wing. Mammoth Hotel cabins are good. Many like the lodging at Canyon but it’s too busy for me.
Day 5: spend today heading out to Lamar Valley for wildlife watching. If it’s hot you’ll have better luck in the cool of the morning. Overnight same. Hiking today would be good.
Day 6: Head to the Canyon area today for views of the Upper and lower Falls from the South and North Rim drives. Drive down thru Hayden Valley to see if there is any wildlife out. Overnight same
Day 7: Head back to Grand Tetons. Overnight either GTNP or Jackson.
Days 8 and 9: Overnight same
Day 10: Flight home. Start planning for the next trip, lol.
I would not book anything non-refundable. I hate to even say this but it may be a big wildland fire year. There may be smoke drift from far away fires. Just something to consider. Put N95 masks on your packing list.
Let me know if I can help. Just a word, I’m currently traveling in Europe (Paris…yea!!) so my response to this thread might be delayed.
Editing to add: Just reread your OP. So are you thinking August 2027? Lodging reservations open with Xanterra/Yellowstone National Park Lodges on the 5th of the month 1 year out…so August 5 2026 for all of August 2027. Disregard the wildland fire caution. Who knows what next year will bring?!?