The Ritz club lounge is not accessible via status in any way. You have to have a club room to access the club lounge. Cash upgrades to the club room vary not just across properties but also for a given property. I've seen various posts on FT quoting $150-500 upgrade charge per night with 200-300 being the norm, which baffles me unless you plan to spend a significant amount of time eating and drinking in the club (which kinda defeats the purpose of being in NYC).

If you can live with just free breakfast instead of the club, the St Regis would be a great option as well.