If you want to create a Japanese themed restaurant, where someone will actually take your order, cook the food, and bring it back to you, I'd recommend you use both that Teppanyaki Grill set with the Business as Usual Bistro set
here. Unfortunately, the cook will use the Bistro oven and not the teppanyaki grill to cook your food, but you can make it so that the guests can only order Japanese food since you can pick the menu for the restaurant.
Without the Bistro set, probably the best you can do is what you just suggested: put a food register, fridge, and teppanyaki grill on the lot. The game will generate a sim to tend to the register, and your own sim or anyone else who visits can decide to use the fridge and grill to cook.
