Without reading rest of thread just yet, I have to correct location of the US Artillery Museum. It is at Ft Sill/Lawton, OK, fwiw. Quite a distance south from Stillwater 
I served three years at Ft Sill and have been to that museum a number of times. LOTS of history to be learned/found there, fwiw. Made me feel rather old to see the Battery Computer System (BCS) I was trained on to repair (as well as Firefinder-related radar system(s). Brought back lots of fond memories. It still chills me to see the ol’ Pershing missile(s) display as there were LOTS of those there when I served, and I feared that one day they would be used somewhere. Most are destroyed now due to a treaty, IIRC.
Anyways, its set up in a ‘timeline-like’ display from oldest types of cannon to current stuff. There is also ‘Atomic Annie’ just around the bend which was designed to fire atomic warheads - BIG gun, that one…
There is also Medicine Bluffs there, which is where the traditional yell of “Geronimo” came from as he was pursued over the cliffs, IIRC (so we were told during boot camp and many times afterwards. Site is/was used for rappeling during my Basic and whenever a day of training was called for. The jailhouse and hospital where Geronimo died is also right there by Atomic Annie, fwiw. I actually did quite a bit of repair stuff in the same room Geronimo died in according to many who worked there. Building is across from Knox Hall right by Fort Headquarters, fwiw. There is another museum dedicated to Ft Sill-area history with all sorts of displays, etc. Also on the Fort is a cemetery of Native Americans who are notable, so if ‘the Old West’ is your thing, lots to be learned/seen there as well.
About 30 minutes away (but bordering Ft Sill to North-side is the Wichita Mountains National Reserve with wild roaming bison,longhorns, prairie dogs, etc and and a great museum there as well, fwiw. You can drive to top of Mt Scott (near entrance to Reserve (free) and view artillery shelling impacts from on-high whenever troops are training (which is very common, IME). I have seen a number of tornado funnels from up there, such is the view! My buddy and I would go up there whenever tornadoes were imminent just to watch 'em. Planty of hidey holes amidst all the big granite boulders that form the ‘mountain’.
IF Ft Sill/Lawton is too far, make sure to go to Sulphur Springs park (in Sulphur of course), kinda middle of townish, hard to miss actually. You can smell the natural springs for miles some days, and lots of folks go to a fountain to collect the water for drinking, etc. Nice park to walk in and/or relax awhile anyways, if that helps, and you can stand the mildish odor of rotten eggs, LOL.
I will remind OP that they will be going through a number of small towns getting to Sulphur that LEO’s are well known to pull over folks for going 27 in a 25mph zone or similar, so make sure to drive through them at posted speed or less, especially if non-Okie plates! Be ready to see LOTS of oil-drilling haulers on road as Central OK is full of heavy trucks that give little room for others on the ‘backroad’ small two-lane highways around Sulphur. Just sayiin’. Enjoy your trip!