One of our listeners, Dane, kindly provided EVEN MORE details about Star Tours. They are below, in (minorly) edited form:
Each ride will randomly select an opening, a first planet, a transmission, and a second planet.
On the ride, C-3PO is on the ship trying to repair the hyperdrive motivator when the auto takeoff sequence is initiated, making him your involuntary pilot. Following this, there are two possible openings:
In the first, Darth Vader, flanked by stormtroopers on the ground and jetpack troopers in the air, swoops in on a flying platform. In a variant, Boba Fett is by his side. He holds out a screen, on which the Rebel spy appears. 3PO tries to fly away, but Vader uses the force to stop the Speeder. R2 activates the weapon systems and two cannons fold out and shoot at Vader, who blocks them with his lightsaber. At this point you fly away and hit hyperspace.
The second possible opening has you rounding a corner in the docking bay and stopped by stormtroopers and a probe droid. In the background, Han is being interrogated by troopers in front of the Falcon. The probe droid latches onto the ship and shows the spy. When 3PO realizes the spy is on board, he and R2 make a break for it and fly the ship away. Han has also made it aboard the Falcon, which you follow, weaving through a bunch of Star Destroyers, until you both hit hyperspace in different directions.
The first planet possibilities are Jakku, Tatooine, Hoth, and Kashyyyk.
Jakku has you following Finn on the Falcon through the battle wreckage, including the Super Star Destroyer (Ravager).
Tatooine is the Boonta Eve podrace, and you inadvertently become a part of the race.
Hoth involves the battle of Hoth (despite clashing slightly with the timeline). There are AT-ATs and snowspeeders.
Kashyyyk has the Wookiees fighting Clone Troopers (Chewbacca is seen briefly as well).
Once you leave the first planet, you receive a Rebel transmission. This can be from Leia, Yoda, or Ackbar, but right now it's locked into BB-8. They ask you to escort the spy safely to a base. R2 is given the information of where to take you. At this point you'll hit hyperspace and arrive at a second planet.
The second planet can be Naboo, Coruscant, or Geonosis.
Naboo starts with passing a Trade Federation blockade. Some Naboo Starfighters have you follow them to the surface, but they are shot down by droid fighters. The droids shoot at you and 3PO makes a crash landing in the water. You then pass by Otoh Gunga, where you either pass Jar-Jar (who ducks out of the way) or in a variant, he gets hit and is sprawled across the windshield briefly. You then follow a Bongo through the planet's core and are attacked by sea monsters before making it to a hanger on the other side. Two variant endings have the pit droid repairing a Naboo fighter doing different things in reaction to your... intrusion.
Coruscant is the battle over the planet, in which buzz droids take out the ship's controls and you plummet to the surface. R2 regains control as you reach the speeder "streets" in the city below (like the beginning of Episode II). There is a variant at the end of this one where Chewbacca and the Falcon are in the hangar when you finally land.
Geonosis actually takes place above the planet in an asteroid field, where you fight Boba Fett in the Slave I. After he sets off some seismic charges, you see the unfinished first Death Star and Vader chases you in his TIE Advanced, flanked by two other TIEs. They follow you into the Death Star toward the core, and when you emerge again, Fett has one more bomb waiting for you, which you deflect back at him before you hit hyperspace to get out of there and to the Rebel fleet and a Nebulon-B frigate.