Then there is a long corridor lined with shops leading to Hotel Villa Fontaine at the end.

At the landing to turn left to Hotel Villa Fontaine, turn right instead and take the escalator (or an elevator) down to level 1.
There are about a dozen restaurants in this area, all spacious and not crowded. I guess not many people come this way.
Unagi Yondaime Kikugawa (うなぎ四代目菊川) is one of them. (But look up its opening hours beforehand.)

MC ordered an Unagi Set, which came with ice-cold yummy sashimi.
 

VT ordered an unagi don, .....
 

.... and a plate of smoked and pickled vegetables.