Malouf's Mountain Sunset Campground http://www.maloufsmountain.com/ near Breakneck Ridge is a great place for camping, and easily accessible from NYC. You can either drive yourself or take Metro North to the Beacon stop on the Hudson line.  It's a hike-in campground, but the guys at Malouf's will pick up your gear, coolers, etc from the train station and pack it in for you.  Then, you can choose from 3 or 4 trail options (30 min hike to 7.5hr hike depending on which trail you choose).  The campground has plenty of space between the platform camping sites, and while it's always good to be courteous after dark, there isn't a strict quiet time.  This won't meet your lakefront criteria, but it's super easy to make happen.  

Another option, depending on your group's budget, would be to check out Cedar Lakes Estate http://www.cedarlakesestate.com/, which is a more luxury "summer camp for adults" type experience if you have the dough to shell out.

Friends of mine have gone to Cold Spring before. You can take the Hudson Line of Metro North and get off at the "Cold Spring" stop. From there I believe you can either take a short taxi ride or long walk to the campground at Clarence Fahnestock State Park. I haven't been myself but it is on my list for this summer. Might be worth looking into! Hope that helps.

You could try Round Valley Reservoir in Lebanon New Jersey http://www.njparksandforests.org/parks/round.html which is about 90 minutes west of Manhattan in New Jersey off of Route 78.  Also not too far from the Sands Casino Resort Bethlehem in Bethleham PA and the Delaware Water Gap. 

My favorite town upstate is Phoenicia, NY and there's a great little campground there called Phoenicia Black Bear Campground. Since the town is at the base of a ski resort, there are groups of travelers of all kinds in and out all the time. In fact, Sweet Sue's is always packed with people eating their signature pancakes at all hours. It's maybe 3 hours from the city, a quick ride, and there are a few larger towns surrounding the hamlet that make it a worthwhile trip, like Woodstock (New York) and Kingston (New York). 

Clarence Fahnestock State Park (Clarence Fahnestock State Park) is a great, convenient spot. Some sites are further from others so noise isn't really a big concern.

If you don't have a car, you can take the Metro North up and a short cab ride (might be $20-30).

Check out the campground at Floyd Bennett Field which just opened a few years ago. It's close to the beach and there are hiking trails too, and the quiet hours don't start till 10pm. More details here:

http://www.nps.gov/gate/planyourvisit/upload/GATE-Camping-Rack-Card-Rules-and-Regulations-FINAL-July2012.pdf 

and here:

http://www.nps.gov/gate/planyourvisit/camp-at-fbf.htm

Sorry, I just saw this now. But for anytime in the future, my recommendations are Hither Hills State Park in Montauk or Cedar Point County Park in East Hampton 

Look into the Adirondack Mountains/ Lake George area. Also Poconos and Catskill. You may also consider white water rafting in the Lake George area-->

http://visitadirondacks.com/recreation/whitewater-rafting

Catskill has some affordable mansions (10-11 rooms) that can easily accommodate groups that large.