Niagara Falls gets a little chilly in January with the mist from the falls, so you'd be best to keep the outdoor activities within reason but ... there are a few great things you can do (and surprisingly cheap).
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Clifton Hill has a great arcade that the teams can compete for tickets and cash them in for carnival prizes, just up the hill there's indoor miniature golf and of course down the hill there's the falls itself.
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Niagara Falls is a great place to do scavenger hunts, you could send the team(s) out plenty of awesome things. Also, be sure to check out https://www.groupon.com/ (not the canadian version, it's buggy) before you come down. The out of season deals are amazing.
I would assume you'd have access to Goat Island if it's open? I've gone a couple times as a child and last year with the Bruce Trail Conservancy during the winter and it was really pretty with all of the ice. I'm sure in the summer time it's even more beautiful with everything in bloom.
You should check out AllTrails: https://www.alltrails.com/us/new-york/niagara-falls
You can download the app and track your hikes as well except you do have to pay a membership fee but I love it. It comes in hand especially if I have no cell service and want to make sure you're on the right trail. I used it a lot on my Arizona and Utah adventures and you just need to download the map before the hike.
Actually, the closest aquarium is in Niagara Falls, NY, just across the border.
Not nearly as impressive as the one in Toronto, but its also much cheaper.
I was scoping out the this spot--an large paved lot. I tried calling the local businesses--the bookstore, psychic, bar, and laundry--to ask if it's Ok to park there, but the phones are disconnected for the former and the line just rings with the latter. I really like the Dufferin suggestion, though I imagine the chances of snagging a spot are slim.
Call ahead and find out for sure. There used to be an odd law that made it illegal to bring a U.S. owned car from a car rental company into Canada, but I think that only applied to Canadians. I also think that law was updated.
https://www.amazon.com/gp/product/B071W7NHJN/ref=ox_sc_act_title_2?smid=A1YNZINGLD2KN3&psc=1
If the car or vehicle is leased, the driver should have written permission from the rental company to drive the car in another country.
You know, I've been thinking about it a little more and while the Lower Niagara wouldn't be ideal for a sloop battle there were several excursions south of the Falls on the Upper Niagara in the Black Rock/Navy Island area. Oliver Hazard Perry's Second in Command Jesse Elliot led a daring raid near Fort Erie and that might make a much more compelling area to set your ship battle.
I recommend reading A Signal Victory for a lot more detail.
EDIT: Awesome, your edit was perfectly timed to my thoughts! Fort Erie held the area above the Falls and was indeed an important part of the story. For your sake I really would read the book I recommended as it's a fairly quick read and will enlighten you.