There are definitely lots of restaurants in the Broadway area, but you should probably call and reserve when you get to New York Most hotels will have visitors guides with ads and phone numbers--or you could ask the concierge to reserve for you.
I'm wanting to try that Angus McIndoe, as I've read good things about.
Last time I was in NY (last spring), I had a decent meal at
Etcetera, Etcetera, on 44th (between 8th and 9th).
I've also eaten at
Blue Fin in the W Hotel, Broadway at 47th.
If you're pressed for time,
Sapporo, 49th and 7th, serves quick, cheap and authentic ramen (I like the shoyu ramen).