If you're looking for shows which depict things that might happen at modern amusement/theme parks, then you could investigate stagings of 'Assassins' (the opening number is set at a shooting gallery) and 'Side Show' (the song 'Tunnel of Love' is set on a ride).
There are other shows which which feature a (to my knowledge) more old-fashioned type of theme park, circus or travelling fair, with depictions of the carnies putting on side shows and acts for the audience to watch. These include 'Carnival', 'On The Town', and the 'Pippin' revival.
I'm not very familiar with most of these shows' stagings, but I know that 'Carnival' uses the show's opening instrumental piece to depict the carnies setting up the travelling fair, transforming an empty meadow into a fairground. The show also has the carnival roustabouts visibly moving set pieces and scenery throughout the show, in character as roustabouts doing their job.
By the way, for those who aren't aware, apparently 'Ride The Cyclone' has recorded a cast album: http://www.emilyrohm.com/blog/an-update-about-my-debut-solo-album.