If you want a VERY casual atmosphere, try Live Bait's calamari (23rd St. across from the park). I'm dead serious! Had some last Saturday after the Big Apple BBQ and it was FANTASTIC! Almost melted in my mouth!
For the past 17 years I've been adoring the Calamares Fritos at El Charro Espanol, 4 Charles Street (Greenwich Ave). I'm a regular there, and I get them almost every time I go. in 17 years, never less than perfect.