I texted my Niece that lives there and she said 4 Charles Prime Rib in west village if you can get reservations.
I'm going to be out there in a few months visiting family and the COTE Korean Steakhouse that
@pearl listed was on my list. I'm going to sell an arm and a leg to pay for it. It's not cheap. šµ
Wherever you decide to go you'll need to be on top of the reservations for your date as none of them take walk-ins unless you're a known local with clout. You should have a list of several possibilities and keep checking as reservations open up and hopefully you can get one for your date.