Monmouth County is located in the central portion of the U.S. state of New Jersey. It is bordered to its west by Mercer, Middlesex and Burlington Counties, to its south by Ocean County, to its east by the Atlantic Ocean, and to its north by the Raritan Bay (sharing a border with the boroughs of Staten Island, Brooklyn, and Queens in New York City, across it). Monmouth County's geographic area comprises 30% water.
I have marked Lot C on the bay side, which is the best combination of parking and access to the water. This spot is very popular with windsurfers. You could also use Spermacetti Cove to the north. On a very fine day, you could even try the ocean side.
This small lake is about a mile long. The only public launch is at the west end in Stevenson Park, off West Front Street. There is a channel from there to the lake, but good luck finding it - be prepared to run aground. Fortunately, the bottom is firm sand, and a short tow on foot will get you out to deeper water. It is also possible to go a short ways up the creek.
Shark River is not really a river, it is more of a saltwater lagoon with an outlet to the sea. The actual inlet would be a very bad place to go, with a lot of boat traffic and sometimes swift tidal current. The lagoon is much better, and I have marked two spots that are easy access and parking - both in public parks. Don't try to use the boat ramp, you might get in trouble.
The Swimming River is an extension of the Navesink. On the map above, you can see the main put-in is at the upper-right in the new (2015) county park. You need to check in at the ranger's hut; there is a ramp fee of $7 per vessel, including kayaks and canoes. The park also has a strict closing time, at which the gates are locked. For details, see the county's page here: