With only one photo scrap in hand, Layton and Luke decide to go investigate the alley blocked by the bulldog and hopefully reassemble the photo.
Food for the Bulldog
At the hotel lobby, you can talk to Krantz for Puzzle 092 and talk to Barton for Puzzle 111, both of which will give you a diary key. If you enter the room upstairs, you will see Flora behaving a bit suspiciously, though she won't tell you why. Leave the hotel and talk to Dawson to trigger Puzzle 062. After that, go to the Cabaret and talk to Ilyana for Puzzle 071, which will give you another diary key.
Return back outside the camera shop and talk to Felix for Puzzle 069. Go inside the camera shop and talk to Joseph for Puzzle 096, which will net you the Sandbox hamster toy. Move up to reach the alley with Precious the bulldog. It will still block your path, but Layton will note that the bulldog seems hungry. You'll need to get some food for it from the grocery store, but you can talk to the new lady in the same scene as Clarice for Puzzle 120, which will give you another diary key.
Move to the top left from here and talk to Marina for Puzzle 075, which will get you another Apple hamster toy. Go inside the grocery store and talk to Garland. He agrees to give you some meat to the bulldog for free, though you'll need to solve Puzzle 074. After solving it, you will not only get a bone-in roast, but it will also get you a Joy Clover Leaf tea set. Check the bunch of bottles near the counter for Puzzle 098. Go all the way back to where the bulldog was. You can talk to Hopper for Puzzle 113, which will net you another Brick Wall hamster toy. Tap on the dog to give it the bone-in roast, which will finally grant you access to the back alley!