At Odione state park, a very short distance North past the main state park, there is a wooden bridge and a put in at the bridge. There are two put ins (one on each side of the bridge). One is part of the park with a fee and restrooms (but not much else), and one is just a parking area across to the other side of the bridge.
Once you put in, go out a short distance going away from the bridge, then go right into a harbor with sailboats and some nice sandy stopping points for exploring. Across from there in the distance you will see the refurbished Wentworth hotel and another bridge. Head past the sailboats to the bridge. Once under the bridge there are some channels to explore with many places to stop the boat and jump on a few rocks. Nice place for kids to stop while on the small islands.
Good introduction to kayaking in a harbor. There are a few things to watch for. Depending on the tide it can be difficult to return under the bridge due to current. After two days in a row I was pretty tired having caught it at near peak both days. Also, watch for power boats when going under the bridge since they share the same path. Plenty of room, as long as you are looking, and just stay to the side. Lastly, a warning that the tide rises quite a bit if you park in the "no fee" area. It is easy to leave your car at low tide and find yourself trapped behind, or in, water. Park up the hill near the grass, or across the street, and you will be fine.
All in all a nice kayak, and you won't be the only one out there kayaking.
Plenty of hotels along the beach road (route 1A).
None if park in the parking area outside the State Park.
Take directions to Odione Point state park, which is on Route 1A in Rye. There are many options to get to route 1A, from Hampton Beach on up or come down from the north. If you enter from Hampton Beach (or route 101, 27, 111, etc.) it is a bit of a drive but the scenery is great and worth the extra time in my opinion.