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.
The musical I’m currently writing (based loosely on “The Cabinet of Doctor Caligari”) has a secondary plot which revolves around a corrupt city council doing everything it can to avoid disruptions to the lucrative town fair, where much of the action takes place.
When it comes to plays/musicals set at amusement/theme parks, one popular option is "Carousel" by Rodgers and Hammerstein. It's all about a seaside amusement park and has lively music, colorful costumes, and energetic dance numbers. Another one is "Wonderland," which is a musical adaptation of Alice's adventures set in a theme park. The stage design and special effects really bring the park to life. Actually, you can just look for a list of the best amusement parks and choose the one you like the most. UPD: sorry, didn't notice the thread is old. Sorry for bumping.
I realize this is a little late for the OP, but several shows feature scenes at Worlds Fairs. Of course in the classic SHOWBOAT, Act II opens at Chicago's White City for the World Columbia Exposition of 1893. ASSASINS features the murder of President McKinley at the Pan American Exposition at Buffalo, 1901. MEET ME IN ST. LOUIS closes at the Louisiana Purchase Exposition in 1904.
In non-Worlds Fair news, Kander & Ebb's STEEL PIER entirely takes place on the Atlantic City Boardwalk in 1933, and SIDE SHOW starts in a traveling circus in the 1920's.
Bruxental said: "When it comes to plays/musicals set at amusement/theme parks, one popular option is "Carousel" by Rodgers and Hammerstein. It's all about a seaside amusement park and has lively music, colorful costumes, and energetic dance numbers."
That's the cheeriest description I've ever heard of Carousel haha