Relentless is right on, do not cheap out on the sewer hose, 10-15' is plenty but for the most unusual situations. I carry a 10'.
1)Make sure you have a breaker bar for your lug nuts and know that the tire wrench fits good.
2) Ice cube trays
3) Plenty of plastic trash bags
4) An outdoor carpet/rug to put down on the ground in front of your door. This is good to take off your shoes, etc.
5) A small doormat for inside so you can wipe them off when you are too lazy to take them off, like I am.
6) Not critical but something I bought and take with was an auto-transformer for low voltage parks.
7) A small cheap voltmeter
8) Even though you are going to a park, put 10 gallons or so in your fresh tank in case your wife wants to stop and use the facilities, you stop for lunch and want to do dishes, your rig breaks down and you are stuck in a parking lot overnight, etc...
9) Carry some tank chemicals, see last item in #8, but you can get by without, I almost never use them unless boondocked for extended periods.
10) Plastic dish rack small that will fit in your sink.
11) you need more than 1 pan and more than 1 pot.
12) tea kettle unless you don't drink tea
13) You said you were going to jersey shore. I assume you have an external H2O connection. Carry a 25' hose with a nozzle. I also carry a Y fitting to hook onto park water so I can hose stuff off without disconnecting. Then you can spray off outside after you get all sanded up and lubed up with tanning oil
15) 30amp to 15/20 amp connector converter.
16) A damn good pair of soft comfortable work gloves. Every good trailer man has a good pair of leather gloves. Wear them religiously, they will keep your hands clean and keep them from getting nicked/scratched up when setting up/pulling out.
17) Enough lengths of 2x6 (enough to span your wheels lengthwise) to block up one side or the other in case your spot sucks and you can't get level side to side. Enough for me is enough to stack two.
18) A 1' level or whatever you have. I have a small one I keep in the rig to set on the counter so that when we unhitch, the wife calls out up or down, and we get it dialed in. I like my rig a little high in the back (head of bed is to back in ours) since sleeping with your head inclined down can be a very uncomfortable feeling but that is just me.
I assume you have all the other usual stuff, this was just the stuff I could think of that did not necessarily make the first trip that we took, but was definitely part of the package by the 5th trip.