Hi Nad,I was in Himeji in 2018, but only visited the castle. The inside of the castle is not wheelchair accessible, as there are many flights of stairs. The outside is partially accessible (you can see the accessible route in the map shared by @ohayotravel), although some of the slopes are a bit steep. As for other places in Himeji, unfortunately, I only visited the castle.
Regarding Mino Falls, I haven’t been there, but I’ve got it on my to go list. When I checked, it seemed that the route from the station to the falls was accessible (around 3km I think), but there were some steep slopes and the way was trending uphill. I remember checking Google Street View at the time (the first bit from the station to the beginning of the trail). Anyway, if anyone has better information, it would be really appreciated.