Places to Paddle
Any place you can put your boat in! You can put in at a boat ramp, sometimes paying a small put-in fee that helps maintain the boat ramp. But you certainly don't need a boat ramp. Check out the waters in your state parks, particularly if you are lucky enough to live near a large body of water such as the Chesapeake Bay or Puget Sound; the state parks provide maps with notations on put-ins, and also where you can park your vehicle.
If you join a club, you'll learn plenty of good put-ins and you'll have a chance to learn from people with more experience too. The day trips they take will give you a good idea of what types of places are available for you to paddle.
If you are exploring new areas on your own, be conscious of boat traffic, wave conditions, and anything else that might cause problems for you. To run into difficulty in strange water is something you seriously want to avoid.
There is a series of books available called Sea Kayaking Along the (you name it) . These are excellent books and will give you great ideas for day trips as well as longer excursions in your area.
The kayak magazines feature information on good paddling spots, but it will be harder to find details on your specific area.
Surf the WWW for personal kayaking websites that might give you some ideas. There is a list of personal pages as well as links to magazines elsewhere on this site.
Don't forget that vacations are an excellent time to explore new waters. There are kayaking outfits in Jamaica and the Caribbean, and for those hearty enough to stand the North Atlantic waters, the United Kingdom and Norway have active paddling communities. Some kayak outfitters sponsor trips to exotic padding locales, such as the Sea of Cortez, the Louisiana bayou and the British Honduras, among many other other places.
If you're looking for something a little closer to home, outfitters and guides offer short local trips in many places in the US.