Established in 1997, The Eureka Casino Resort offers the best accommodations, dining and gambling options in Mesquite. Nevada. The Casino offers guests over 1,100 slot machines, table games, sports book poker room, and bingo. The Eureka Casino Resort features three restaurants and over 200 rooms and suites. With a convenient location, this relaxed, modern casino resort with mountain views is 3 miles from Palm Golf Club.