Jersey aquarium huh? Few suggestions:
First of all, what size tank did you have in mind? To really get the most out of it I would suggest nothing less than 90 gal. With a 90 gallon tank you can really do a lot more stock wise than with something like a 55 or 75 gal. All the necessary equipment such as a filter, lights, and powerheads (good circulation is crucial) along with a protein skimmer would be a good start.As for your substrate you could use sand you get at the beach if you really want to "jersey" it. Sand around here is a little darker and would give you a more local feel than white calcium based sand. Be sure to "wash" it with fresh saltwater to get the cruddy ocean scuz out. One problem you may run into with NJ sand is pH balance. Sand around here is silica based if I'm not mistaken. The play sand/crushed coral in more tropical tanks provice pH balance. You can monitor the tank closely though, and adjust the water chemistry as needed. Slate, concrete, or jetty rocks would also make additons to create your little "reef"
As for livestock, simply remember that you can have 1 inch of fish for every 10 gallons of water. So in a 90 gallon tank you could have a 9 inch eel or 9 individual 1 inch baby fluke. I'm not sure on the supply of aquarium sized fish you'd find in NJ from a retail perspective, remember however that if collecting live specimens a 2 inch baby fluke is not OK to take even though you aren't killing it. There are, however, tons of local species that have no restrictions and a simple trawling net close to a jetty would provide excellent specimens of both fish and suitable invertabrates.
This site is excellent on aquariums, and I used it to set up my own saltwater tank, http://www.aquariacentral.com
A final note though, marine aquariums are not a cheap hobby, almost as expensive as diving .
Also, Allenhurst Jetty was that bad? Must be a winter thing, in the summer its a beautiful location, conditions can be a little unforgiving though.