Mooring your boat will be less expensive than a slip in a marina. With a mooring you will not have running water, nor will you have electricity available. How much electric and water will you really need during the season is a question only you can answer. If you are like myself, our boat is pretty self sufficient. We have a solar panel to keep the battery charged, an alternator to charge the battery while under power, and water has never been an issue. We do maintain a 10 gallon tank on board, but find this is mainly used for washer your hands. For cooking, coffee, or tea we use bottled water and always have a very good supply of that on board. If I need to do repairs and it requires more than my cordless power tools can provide I bring my small generator out or use my 700 watt inverter to get the job done. The biggest problem you will have with a mooring is the ease of getting to and from your boat. On a dock you can step right onto your boat, but the mooring will require a dinghy or launch service. A launch service is usually only available at yacht clubs where your either pay for it in your dues or pay for it as an added expense. I prefer to use my own dinghy which allows me more freedom. When you use a dinghy you may leave the dinghy tied to your mooring ball or you may decide to take the dinghy with you on your sail. Sometimes we do take the dinghy with us if we plan on having to go to shore or if we have planned to stop and eat someplace where a dock may not be available.
A mooring ball is a large round ball that floats on the surface and usually has a chain attaching it to a large mushroom type weight on the bottom. When these weights work their way into the bottom they become very difficult to remove due to the suction they have in the sand or mud. Some use a pendant from the chain to their chocks on deck and others use the chain directly to the chock. Granted the pendant will be much better to your boat than a chain, but you really have to monitor the wear on these pendants. They do offer abrasive resistant sleeves that go over the pendant, but they don't last for ever. To leave your mooring you should have your sails up already or your motor started depending on how you will be traveling. You would attach your dinghy (if leaving it) and then drop the chain or pendant, and off you go. To get back on your mooring you need to note where your mooring is so you don't pick up on another persons mooring. With each mooring is usually a float with a 4' or 5' fiberglass whip with a light nylon line to the chain so you can grab it from the deck without having to use a boat hook. We place a flag on ours so it is easy to identify as you come into the mooring field.
Now that you have a reasonable idea of how a mooring works we can discuss where you can find these moorings. At least in Raritan Bay you may not put in a mooring wherever you choose. There are fixed areas so that you do not disrupt boat traffic within the bay. However there are a number of places throughout the bay area where a mooring is available.
1) Atlantic Highlands offers a protected mooring field - http://marinas.com/view/inlet/709_Atlantic_Highlands_Inlet_NJ_United_States
2) Keyport Harbor offers a nice harbor mooring field - http://www.keyportyachtclub.com/ or you may contact Olsen's Boat Works who takes care of the harbor moorings
3) Perth Amboy is at the back end of the bay - http://www.ryc.org
You may also find moorings available up some of the tributaries that feed the Raritan Bay. Most will require you to go under bridges to get out to the bay. This can be a real pain at times and I prefer not to deal with any bridges or anything for that mater that may infringe of my sailing.
I will throw this out there for what it is worth, Olsen's Boat Works in Keyport is the most reasonable cost for moorings. The place is a no frills yard and you should not rely on the yard for supplies, water, rest rooms, gasoline, or anything like that. It is the real basics of putting your boat in and out and setting your mooring, which they will provide. You may also be able to arrange for winter storage there.
Lots of luck with your sailing and mooring.