Nanjya Monjya, Waterfront Plaza
This is one of the few places in Singapore that has multiple teppan grills for making your own yakisoba (stir-fried noodles) and okonomiyaki (a Japanese pizza of sorts - literally, "things you like to grill"). Unfortunately, we were stuck with an outside table as they were all full, so they had to make our food for us, and the okonomiyaki wasn't quite done as greasy as I would have liked. But this is probably one of the more authentic and down-to-earth Japanese places around town. They have a very extensive list of dishes too, ranging from simple hiyayakko and zaru soba to even nasu dengaku, which is basically half an eggplant baked with miso, creating a pretty uniquely warm and mildly sweet taste.
Anyway, the photos here don't really do it justice (sorry, we were sitting outside with poor lighting), but this place is worth coming to if you want some greasy Japanese food. It's at 392 Havelock Road #01-03 (6738-7177), with another location at the Allson Hotel, albeit without the do-it-yourself grills.