A fine place to meet, have a drink, or just sit a spell, the casually elegant lobby at the Fairmont Algonquin is located between the check-in area and the restaurant at the far end. Some nights a professional piano player performs.
Off to the side (white doors on right), there is a computer with Internet access. The service is free, but it's also slow. My recommendation: If getting online is essential, lug a laptop and pay for the much faster in-room access.