Full disclosure - I have been to none of these campgrounds.  But, I did some research in preparation for a last minute camping trip and this is what I proposed to my travel companions (all have availability as of July 21st for next weekend):

about 2 hours; KETTLETOWN STATE PARK, CT: http://www.reserveamerica.com/camping/Kettletown_State_Park/r/campgroundDetails.do?page=details&contractCode=CT&parkId=100109&topTabIndex=CampingSpot 

about an hour and a half; WILDWOOD STATE PARK, NY (long island): http://www.reserveamerica.com/camping/Wildwood_State_Park/r/campgroundDetails.do?page=details&contractCode=NY&parkId=288&topTabIndex=CampingSpot 

about 2 hours; LAKE WARAMAUG STATE PARK, CT:http://www.reserveamerica.com/camping/Lake_Waramaug_State_Park/r/campgroundDetails.do?page=details&contractCode=CT&parkId=100110&topTabIndex=CampingSpot

about 2 and a half hours; LITTLE POND CAMPGROUND, NY http://www.reserveamerica.com/camping/Little_Pond_Campground/r/campgroundDetails.do?page=details&contractCode=NY&parkId=495&topTabIndex=CampingSpot - apparently a really nice lake and not a pond at all