Gezellig is comfortable, but also lively: it goes deeper than mere coziness. It's all about a sense of belonging--in this way, it's a near antonym to another untranslatable word, the Portugese saudade, which connotes an existential homesickness.
Wikipedia defines gezellig like this:
Gezellig is very colloquial, and is most often used in these contexts: one is with family and/or friends, light is right, people are right, music is right, conversation is right, then the feeling is "gezellig". So, a fantastic combination of cosiness, enjoyment, relaxation, well laid-back at home or chilled-out in a bar, while being in good company, is "gezellig".
As a city, New York has travelled awfully far from its Dutch roots, but I think all those donated daffodils and tulips might be effecting a rapprochement. To my mind, one of the things that the success of Apartment Therapy signals (the other is that the Ryan Bros. and SK are very smart cookies) is that we're interested not just in commerce but in community, not just in buying well but in living well.
So, sharks and snarks, please move along: here we're more into tolerance and goodwill. We're Dutch like that.