I live in this neighborhood, have belonged to the Equinox at Columbus Circle, and now belong to the Reebok Sports Club (part of the Sports Club/LA chain). No question that Reebok is nicer than Equinox. I believe that guests staying at the Phillips Club (one of these executive-stay, boutique style hotels) have privileges at the Reebok Sports Club, but it's a block and a half walk.

Neither of the other Sports Club/LA gyms in NYC are attached to a hotel like the Boston Common Ritz Carlton.