No reason a ready room or Captain’s Office couldn’t have been just down the next deck from the bridge. Just because we never saw one used doesn’t mean it wasn’t there. Maybe Kirk opted not to use said office and had it repurposed for something else.
That works! Franz Joseph's Deck 2 science labs don't all have to be right there. Although I will say, FJ ensured that there are fourteen science labs aboard this ship. The finest equipment and computers in the galaxy. So anything you clear out of Deck 2 needs to be worked in someplace else.
I would be willing to say that the bowling alley was just a joke on Riley's part, and the space it occupies could be used for things that matter.