Welcome to Buffalo, Jaci! One casino in Niagara Falls, about 20 minutes north of Buffalo. Seneca Niagara is the name. Two more right across the border in Canada, if you feel like venturing across the bridge. There is a smaller, temporary Seneca Casino in downtown Buffalo, but it's not much. If you're staying south of the city, there is one at the racetrack in Hamburg. The Seneca link below has links to all Seneca casinos. The third is 90 minutes south of Buffalo.
http://www.senecaniagaracasino.com/
http://www.the-fairgrounds.com/hamburg-casino