I haven't been in a while but used to go there quite often with my ex husband who was from Upstate New York. We always ate at Cavallario's Steak and Seafood (one time we got an 8 pound lobster! yum!) The antique boat museum in Clayton is really neat and I loved going to Boldt Castle on Heart Island. Definitely take one of the boat tours of the islands.
We never went to Singer Castle so I can't tell you much about that. We would also go to the park in Alex Bay and just enjoy the weather and picnic. Lots of cute little shops are in that area too.
Once we got crazy and took the wave runner from Alex Bay to Ogdensburg. It was nuts! Riding alongside those huge tankers and ships was terrifying!
Have a great time -that place is gorgeous!