Restaurants have to allow trained service dogs but a two month old puppy is not a service dog and it would be illegal for the restaurant to allow the puppy into an inside seating area. They didn't really seem to have any outside seating so my hunch is that your puppy would not be allowed but you could call and ask keeping in mind your puppy is not a service dog.
I wouldn't recommend it, you need to take an elevator to the third floor, and balcony seating is very limited.
Maybe, it's on the roof but there are tables "outside" area....
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