Since OP will be staying at the Andaz, I would highly recommend
Anpuku in Toranomon Hills. Their main focus is fusion-style udon noodles, but you can also get charcoal-grilled meats and fish and other upscale izakaya-style dishes.
They also have a very nice selection of maybe two dozen craft sake from around Japan, and you can optionally have them served in small-size tasting glasses, so you can try several different types of sake during your meal.
Anpuku is in the Toranomon Hills shopping complex, where the Andaz is located, and there are lots of other restaurants there as well. I'm not sure what days they will be closed for the holiday though, so check their schedule ahead of time.