find out whether there are any places in New York that sell dairy-free cakes and milkshakes

I’ve just been diagnosed with a dairy allergy, which means I can’t eat anything that has butter, milk, cheese or any other kind of dairy produce in it (apparently whey is out of bounds too). So, the ultimate challenge…can I find a dairy-free milkshake in New York?

Obviously I don’t live there, but I’m about to go to NYC at easter and it’s a more interesting challenge than finding one here in England. Aha, but then there is room for expansion and sequel goals!