I'm working on my current fic, where Miyasaka decides to go off to a nightclub alone after Katou and Onozuka abandon him in favor of their lovers. They had previously been at Lime, which the manga says is located in Ginza, so I was just doing a quick web search on "Ginza" to get ideas, and I found this entry for Lime:

Lime is a popular "aquarium" lounge bar. If you come as a couple and are lucky enough, you might be seated in front of the aquarium, which is 20m long and houses 2,000 tropical fish. If you come with friends, you'll probably be seated in the Southeast Asian-themed area of the bar. In either case, you'd better book ahead.

Pretty cool, huh? I guess that the Lime in Haru probably refers to this club. We haven't seen the aquarium, but since Katou and co. seem to be seated in a private room (in Book 13), it probably wouldn't be visible from where they're sitting.

Also, in case you didn't see the entry on my personal journal, there is a sushi restaurant called Katsuya in Brentwood in Los Angeles.