I've taken so many girls out on dates to arcades in Japan. Luckily they're usually divided in areas so we go to the parts with the print club picture machines and the UFO catcher machines.
There's a really big one close to where I live that's right below the movie theater and it's really awesome. It's divided into an area with kids' games (Tetris, Mario Kart, etc.) and print club booths, another area for the UFO catcher stuff, another area for the coin machines, and another area for darts and fighting game and Beatmania/shmups/hardc0r gamer stuff.
Take a girl to the movie and then spend a half hour at the game center before going to dinner.
