Help! In desperate need of great coffee near 36th & 5th
That's an area devoid of cafes (aside from Starbucks).
If you want tea, there's Subtle Tea on 30th and Madison. But it may be a bit too casual for what you're looking for.
There's Franchia for tea, but it doesn't open until lunch. Le Pain Quotidien may work for you -- but also casual. Koryodong Bakery (Korean bakery) on 32nd between 5th and Broadway is probably the best bet for what you're looking for near your client's office.
Les Halles and DB Bistro are both open for breakast, and probably the most ideal in terms of a business meeting. But it's a bit far from your location.