Hi,
I sometimes have trouble distinguishing whether this is a situation requiring a plural noun or not.
He gives the children a chance to 'show off' their own town (how about towns???), and be the experts (how about experts???) on familiar territory.
When I see this kind of sentence, my attention seems to be on the word "children" and have a hard time thinking it otherwise. I believe that the use of the term "their own town" would be appropriate if they all have the same town and it seems that being the case here is unlikely. How about using these variations?
show off his or her town ?
show off their own individual town?