The Julian Restaurant sign.
Julian Restaurant is a restaurant that can be found in Academy City, with waitresses serving meals such as breakfast and even desserts.
There are at least two known branches of the restaurant that can be found in the anime adaptation. One of which is notable for being the same restaurant that both Accelerator and Kamijou Touma went to on the same day.
Chronology
Toaru Kagaku no Railgun
Mikoto in front of restaurant, as seen in Toaru Kagaku no Railgun.
In the Toaru Kagaku no Railgun anime adaptation, the restaurant is seen during Misaka Mikoto's complaining to Uiharu Kazari, about Shirai Kuroko's recent lecture of her sticking into Judgment business. However, their conversation is interrupted by the arrival of Kuroko who takes Kazari away for Judgment work. However, Kazari forgot her Judgment armband, which gave Mikoto an opportunity to disguise herself and experience being member of Judgment firsthand.[1]
In the manga the restaurant used for the scene was Joseph's Coffee and Restaurant instead.[2]
Toaru Majutsu no Index
Another restaurant is used in the Toaru Majutsu no Index anime adaptation during the Three Stories Arc, here, Accelerator brings Last Order with him for breakfast where he later sees Amai Ao, who immediately leaves the vicinity after seeing Accelerator. Last Order later confronts Accelerator regarding his true feelings towards the Radio Noise clones he killed for the Level 6 Shift. Accelerator immediately after Last Order's conclusion that he really didn't want to kill the clones at all, though not before seeing Last Order collapse from an apparent illness. However, Amai Ao later arrives and pretends to be related to Last Order and kidnaps her.[3]
The same restaurant is later visited by Touma and Index for a meal, where they are later attacked by Yamisaka Ouma who kidnaps Index. Touma is then forced to give chase.[4]
Much later afterwards, Accelerator revisits the restaurant after being informed by Yoshikawa Kikyou of the danger Last Order poses to the world; he discovers that Amai Ao took Last Order after pretending to be related to her. He later calls Kikyou to inform her this, where he discovers from her that the traffic flow to and from the city has been frozen due to a security breach. Because of this, Accelerator is able to predict where Amai Ao would be hiding.[5]
Both scenes with Touma and Accelerator uses a different restaurant in the manga adaptation.