Adereth El on East 29th Street between Third and Lexington. (It has been at that location for over 150 years.) Their website has the times of services.
The closest to 46th Street and 2nd Ave according to Godaven.
Beit Yitzchak Ohel Sarah Synagogue (sefardi) -587 Fifth Avenue (between 47 & 48 street) New York, NY 10017 USA (212) 750-5000 – says there is Shacharis M/Th @ 8am.
Chabad of Midtown (see above) is next closest for Shacharis.
I think there are minyanim by the diamond district by the dairy cafe there – but it’d might be only Mincha.