Wait until you can cross the border. The American side is not nice.
I think Goat Island is great, and a wonderful place to walk around and take pictures.
Did this while visiting my parents over Thanksgiving on a whim. We don't have passports and its not like the good old days where crossing the Rainbow Bridge, especially for WNYers was a simple verbal attestation of citizenship.
The Niagara Falls State Park was very enjoyable and without the commercial tourist trap of Clifton Hill on the Canadian side. Growing up in WNY, we most often went to the Canadian side. We also had some nice rainbows appear while walking down near Terrapin Point on Goat Island from the waves of mist and the setting sun that G4 and G14 were amazed with.
Also recommend for anyone with a Notre Dame affinity and a little adventurous to stop in at Gadawski's on Falls St. Most of the immediate neighborhood residences have been taken over by Niagara Falls Redevelopment and vacated, and the area is a little sketchy, but having been there once to watch a game, it is a true Notre Dame tavern with good Polish food. Eddie Gadawski is a die hard subway alumnus and a treasure of memories.
The whole area is very beautiful in the snow, but there's not a whole lot of action around after 6pm or so. Just a lot of boredom and, I suppose, alcohol to pass the time. The American side is about the same but a lot lighter on the beauty.