Is it a reasonable day from Neustadt an der Aisch, to combine Bad
Windsheim for the open air museum during the day and Rothenberg ob der
Touber for the evening - to do the night watchman tour and return to
Neustadt an der Aisch for the hotel?
Last train of the day out of R'burg is typically 22:06, arriving Neustadt (Aisch) 23:35. Check the DB site for your date. I have not combined the two myself in one day but I think it's doable with a full day.
The Nightwatchman tour was mildly entertaining but a tad hokey IMO, not worth staying late if you don't wish to, and watchable on youtube. That said, I could tell some of the other participants were quite engaged.
Note that Neustadt(Aisch) has 2 stations - "Bahnhof" and "Mitte" - so on the DB site, check the schedules for the station that is nearest your accommodations.
Bad Windsheim is only 20 train minutes away from N'stadt so it probably would work OK as a base for your outings - check the schedules - and of course the Freilandmuseum would not require an outing at all if you stay in Bad Windsheim.