New York
In case any of you may be travelling to New York in the near future, I have two recommendations.
1. Serendipity. Home of the frozen hot chocolate (big enough for 2-3 people), and plenty of other ice cream/dessert treats. Five out of Five stars. (The only negative is that you need to put your name on the list about 3 hours ahead of time, because the guys that own/run serendipity refuse to expand or even offer "To-Go" services, so there's always a huge wait, even though there are always several tables open at a time.)