Which characters unlock each scene?

Food Levels

• The Cantina -> Han Solo or Greedo
• Mos Espa Cafe (the first scene) -> Gungan or Gran
• Ithorian Food -> Ithorian
• Scoop of Hoth -> Snow Trooper (Fixed in 1.3.0 update)

Service Levels

• Bounty Hunters -> Boba Fett or Dengar or 4-LOM or Gand
• Cloud City Spa -> Han Solo or Boba Fett
• Trash Compactor -> Luke or Han or Chewbacca or Leia
• Panna City Medicine -> Boba Fett (Holiday Special)

Recreational Levels

• Holochess Hall -> IG-88 or Chewbacca
• Holonet Cineplex -> Chadra-fan
• Imperial Museum -> Ewok or Snowtrooper or Wicket
• Mon Cala Aquarium -> Mon Calamari (not Admiral Akbar)
• Training Remotes -> Obi-wan or Luke

Retail Levels

• Droid Store -> Greedo or R5-D4 or Jawa
• Imperial Marches -> R2-Q5 or R5-J2 or R4-I9 (Service to the Empire Special edition droids)
• Watto's Wares -> Pit Droid or Toydarian or Watto or Gungan

Residential Levels

• Dagobah Apts -> Yoda or R2-D2
• Tatooine Apts -> C3PO or Tusken Raider

Imperial Levels

• Blast Door -> Obi-wan Kenobi or Darth Vader
• Communications -> Han Solo or Luke Skywalker or Chewbacca
• Detention Level -> Luke Skywalker or Han Solo or Leia Organa or Chewbacca
• Droid Lab -> Leia Organa
• Extending Bridge -> Luke Skywalker or Leia Organa
• Imperial Meeting Room -> Darth Vader
• Interrogation -> Leia Organa or Interogation Droid
• Superlaser Ray -> Imperial Gunner
• Tractor Beam -> Obi-wan Kenobi or Snowtrooper (new patch)
• Sith Meditation -> Darth Vader

By Character

• 4-LOM -> Bounty Hunters
• Bespin Leia -> none
• Boba Fett -> Bounty Hunters, Cloud City Spa
• Boba Fett (Holiday Special) -> Panna City Medicine
• C3PO -> Tatooine Apts
• Chadra-fan -> Holonet Cineplex
• Chewbacca -> Trash Compactor, Communications, Detention Level, Holochess Hall
• Darth Vader - Imperial Meeting Room, Sith Meditation, Interrogation
• Dengar -> Bounty Hunters
• Greedo -> The Cantina, Droid Store
• Gungan -> Mos Espa Cafe, Watto's Wares
• Han Solo -> Communications, Detention Level, Cloud City Spa, Trash Compactor, The Cantina
• IG-88 -> Holochess Hall
• Imperial Gunner -> Superlaser Ray
• Interrogation Droid -> None
• Ithorian -> Ithorian Food
• Jawa -> Droid Store
• Leia Organa (Rebel) -> Interrogation, Extending Bridge, Droid Lab, Detention Level, Trash Compactor
• Luke Skywalker -> Extending Bridge, Detention Level, Communications, Training Remotes, Trash Compactor
• Mon Calamari (not Admiral Ackbar) -> Mon Cala Aquarium
• Obi-wan Kenobi -> Blast Door, Tractor Beam, Training Remotes
• Pit Droid -> Watto's Wares
• R2-D2 -> Droid Lab
• R2-Q5 -> Imperial Marches
• R4-I9 -> Imperial Marches
• R5-D4 -> Droid Store
• R5-J2 -> Imperial Marches
• Scout Trooper -> Imperial Museum
• Snow Trooper -> Tractor Beam, Scoop of Hoth
• TIE Pilot -> Superlaser Ray
• Toydarian -> Watto's Wares
• Tusken Raider -> Tattoine Apts
• Watto -> Watto's Wares
• Wicket (not Ewok) -> Imperial Museum
• Yoda -> Dagobah Apts

For your printing and tracking pleasure, as of game version 1.3.2700 (2014 January 18):

It seems the Wikia wiki is kept reasonable up-to-date:

http://tiny-death-star.wikia.com/wiki/Scenes