Two Hands-Manhattan
Two Hands is an Australian Cafe with a few locations around NYC. They also have some locations in other cities too. Their Tribeca location had a nice outdoor seating setup that was dog friendly. They serve a delicious brunch with some truly amazing food that is worth a little splurge. The outdoor seating does have a roof and heaters for when it is cold but open walls so if it is rainy or windy and cold, it can get quite uncomfortable.
This spot gets 3 paws because the outdoor seating isn't the most comfortable if it gets cold or is rainy.
Dog Seating:
Covered and heated outdoor seating.