Hotel lobbies are the perfect balance of public and private for me.
I get to not feel like a shut-in, but also have privacy to read, work, or listen to music. They also usually have good access to food and drink, restrooms, and often public wifi.
But more importantly, in a hotel lobby, no one judges you if you mind your own business. No one interrupts you. No one asks you questions because everyone assumes you are from out of town. It's rare to find the confluence of productivity, public interaction, and comfortable solitude that a good hotel lobby provides.