I believe you can get either take a public bus or a hotel bus to Buffalo/the Falls/your hotel from the airport. There is no metro from Buffalo to the Falls.

There is not much on the American side other than the Falls and the State Park. There is a small aquarium that is Ok for smaller kids.

There is much, much more to see and do on the Canadian side. The view of the Falls is much better on the Canadian side. You can walk across to Canada on the Rainbow Bridge but you will need passports/passport card/enhanced drivers License.

Not a lot of choices to stay in Niagara Falls. There is a Hampton Inn, Sheraton, and the Seneca Casino all within walking distance of the American side of the Falls. There may be a couple of more. Many more choices on the Canadian side of the Falls.