I davened weekday Minchas at the Tribeca Synagogue on White Street and also the Wall Street Synagogue at 48 Beekman Street, apparently near your Hotel, but was never in that area on Shabbos. I always thought the latter was closed on weekends, as all the other weekday financial district Mincha minyanim, but I just googled the WSS and they show Shabbos services. Also, if you’re up for more of a walk there are Shuls on the Lower East Side, but again I’m not familiar with any details.