Parking near the falls (on either side of the border) can be outrageously expensive ... that's if you can find a spot at all. 

If you can, leave your vehicle at the hotel and walk ... but WEAR COMFORTABLE SHOES

Transit in Niagara Falls, NY and Buffalo, NY is provided by the NFTA. There is no longer direct public transportation between Niagara Falls and Buffalo Airport (25 miles away) -- the previous NFTA route has been discontinued.

The seasonal (May to December) NFTA Trolley route 55T does connect downtown Niagara Falls with the low-traffic Niagara Falls International Airport (7 miles away). See route details and map.

The Niagara Scenic Trolley will take you around a three-mile route within Niagara Falls State Park, making stops along the way. For a bargain price ($2 adult/$1 child) you receive an all-day pass that allows you to re-board as many times as you wish. 

For public transit on the Canadian side, see TripAdvisor's page Niagara Falls, Ontario Public Transportation.

Bicycle is actually a great way to travel in this city.  If you can bring a it!  The recreational trail along the Niagara River takes you to numerous attractions, and you won't find a better trail anywhere.  A few tourists have those "fold up" bikes; they're really glad they brought them.