When I boated on the North Shore, next peninsula west (Smithtown Bay), we had a blast tubing with my then young children. I did trailer then with a 19 foot Center console and then a 24' Bayliner that had a nice cabin and an enclosed helm.
If anchoring out, chilling, visiting the beach and tubing is what you want to do, then you should be in good shape. Shooting across to CT is definitely doable. Smithtown has two beaches (Long Beach and Short Beach)both nice, I preferred Short Beach.
Port Jeff has a nice protected cove due east of the harbor entrance, also a nice place to chill. We use to go to a restaurant in CT, forgot the name but it was straight across from the last buoy coming out of Smithtown Bay.
Basic difference for your type of boating is the North Shore has rocky beaches as opposed to sand on the South Shore. The North Shore is less congested and IMHO has more of an open space to tube and water ski.The North Shore has less places that are a hop skip and jump away. North Shore you deal with rocks, the South Shore we deal with skinny water.
As far as mooring you boat goes, be prepared to deal with seagull crap

Maybe you could find a local yard or place you can store the boat when your not using it.
Also,
Get the kids into fishing, there is great bluefish, stripper, fluke and black fish fishing between Port Jefferson and Huntington.
Best of Luck
Walter