If you are in NJ you can start at the boat ramp that the town of Penns Grove has at the end of Railroad Avenue. Penns Grove is Salem County NJ. The ramp is not in great shape but easier than climbing over the rocks at the end of Main Street into the Delaware.
Choose a day that is not too windy so there are no white caps. If you go with the tide going out you can cross the Delaware and wind up very close to the entrance of the Christina River, which will take you up to Historic Wilington, and the Brandywine River as well.
At the mouth of the Brandywine there is a restaurant, boat ramp, (Up The Creek). Up The Creek may not be open in the winter, so call first if you plan to stop there. If you go further up the Christina you will see the Amtrak train station, The Wilmington Rowing Club, and some other interesting stops.
I would allow 4 hours for the trip. 1 for each crossing the Delaware and one for going up and down the Christina/Brandywine.
I use an Ocean Kayak, Malibu 2, sit on top which I have been quite happy with. I bought it at Jersey Paddler in Toms River NJ.
Anyone interested in kayaking in the South Jersey, New Castle (Northern) Delaware area please email me! firstname.lastname@example.org. If you visit my site at http://www.schlimme.com I will try to post my recent trip pictures.
PS. - The Delaware River does have heavy freighters so be aware of your surroundings. They are usually a few miles apart, or between them.