28 HongKong Street should fit your bill. It's a well-regarded bar near Chinatown with great drinks and a good food selection and vibe. They might take reservations; I don't recall, but try to get one if they do.

D. Bespoke is a great bar as well. It's Japanese-inspired, somewhat formal, quiet, and expensive. Very different scene than 28 HongKong Street, but I highly recommend both.

None of these place have outside seating.

I haven't been to Tippling Club, but that might be another option.
You can also wander around on Amoy and Telok Ayer Streets. Jigger & Pony is a good bar. I just saw that Employees Only is there too. Their NYC location (the original) makes great drinks.

Have fun!