Boldt Castle is the main attraction for many 1000 Islands' visitors. It's only accessible by boat--but Uncle Sams Boat Tours provides ferry service throughout the day (as well as a number of other fun boat tours and excursions).
Yes, there is another castle. A slightly longer (but beautiful) boat trip. Again, Uncle Sams Boat tours provides tours to Dark Island, where Singer is located. There is also a shuttle service available from Schermerhorn Harbor, about a 15 minute drive from Alexandria Bay.
There is no better way to see the 1000 islands. There are many boat rental companies in the area. They offer pontoons, fishing boats, regular motor boats, as well as paddle boats, kayaks, stand up paddle boards, and who knows what else. Some companies to look into for rentals: O'Briens boat rentals, Schermerhorn Harbor rentals, Swan Bay Resort rentals, and Mac's Boat Rentals.
Clayton is cute town about 20 minutes down the river from A-Bay. There are lots of cute stores, restaurants, and, of course, a beautiful waterfront (great place to catch a sunset that Trip would judge Grace for photographing). There is often live music on weekends, and a very cool antique boat museum (actually, it's very cool).
The US and Canada share the St. Lawrence River and roughly half the thousand islands are Canadian. Alex Bay is just about the last exit off the highway before you get to Canada, so it's easy to head up north (especially if you have a little extra time). There are some great nearby Thousand Islands cities and towns (Kingston, Brockville, Gananoque), and if you're really making a trip of it, Ottawa is about an hour and a half drive and both Montreal and Toronto are about three hours. There are also many boat tours that will take you through the Canadian Islands if you're interested (again Uncle Sams, and Clayton Island Tours as well). If you plan on getting off on Canadian land, make sure you bring your passport (boat tours that don't dock won't require one).
The most important activity in our opinion. What else are rivers for? Here are some places to get in the water (and if you struggle at all with this, let us know!): Alexandria Bay Town Beach (tiny, walkable from downtown Alex Bay), Kring Point State Park (short drive from Alex Bay), Grass Point State Park (short drive from Alex Bay), Wellesley Island State Park (slightly longer drive onto one of the biggest islands on the river--very cool park). Let us know if you need to borrow tubes!