What, specifically, are you looking for? Also, did you see all of Urban Square? There's more than just the claw/trivia games on the first floor - the upper floor has two different rooms full of fighting/card games and some other things.
To be honest, most of the arcades in Japan all seem to have the same stuff no matter where you go, really. The arcade in Aeon (at least the Nagoya Dome one) is pretty much the same stuff, although it's a bit nicer aesthetically.
If you're looking for an 'old school' arcade, there might be some in Osaka or Tokyo... but I've never been to one in Nagoya. Do check out the Round 1, though - I never made it to there, so I don't know what that ones like.
Also, if you can read Japanese, this site will help you track down all the game centers/arcades in Nagoya (or anywhere else).
Ge-sen