1 place I recommend
This is the one place in Kobe I have eaten at myself and would recommend.
The Sannomiya branch of Kobe's celebrated Mouriya, serving premium Kobe beef teppanyaki since 1885. Watch your steak grilled before your eyes at the counter. The largest of the Mouriya group, a short walk from JR Sannomiya Station.
Address: 1-chōme-9-9 3F, Kitanagasadōri, Chuo Ward, Kobe, Hyogo 650-0012, Japan