There is a nice turf field on the JHS campus (20th & Indiana) but they play their games at Junge Field which is a stand alone facility a few blocks west of Main Street on 13th/Junge Blvd - it's kind of an odd spot to get to.
In the Joplin area the two must sees are Joplin (historic, unique) and Webb City (large seating, noteworthy program). Next I'd add Carthage (new nice setup - building indoor facility next to stadium) and then CJ if you have time, which btw is practically next door to Webb City so why not. You could easily get all of these in a loop. Neosho is about 30 min south if you had more time to spare.
A few others that come to mind in the larger SWMO area - Mt Vernon, Ozark, Republic, Branson, Reeds Spring. Maybe Monett as well. Sarcoxie has a new turf field. It would take a long time to get to all those though esp Branson and Reeds Spring.
The stadium where PHS plays in Pittsburg KS is an old rock stadium that is kind of cool. I think it's at the Jr High not the high school. If you did make the trip over there the bigger attraction is PSU's impressive D2 facility.
I have no idea about NE Oklahoma.