you might be able to get temporary docking up near barnegat light or loveladies but most places will charge you. unless you can find someone willing to keep it at their residential dock in the lagoon or something. another idea is to go out to the break in barnegat that is super far out, and anchoring there, ive heard of people doing that
In both dewey and oc I've anchored jet skis real close to the beach for a day and they were fine- I assume they're newer skis with an actual key instead of just a plug. just make sure your good with the tides.
Most marinas usually charge by the length of the vessel/hour. That might be a safer way to go and I can't imagine it costing too much.
yeah, anchoring would be your best bet. i recommend the break thats out off barnegat light because its so shallow out there you'll be able to surf and keep an eye on it. that or anchor it on the end of the island by holgate