A nice trip, be sure to see Devils Tower on your way west of the Black hills, then on to Cody.  2 places to stay in
the park are at the Yellowstone Lake hotel or cabins, be sure to eat at the dining room there,  Then stay at Old Faithful
and enjoy the lodging and restaurants there.  We stayed at both in May of 2022 right after opening, and they were still
recovering from covid, so things were slower.  Food is important to many of us, be sure to reserve a table in advance.
In September, things will be busy, so get things booked.
Enjoy your trip.