Location: Westport 419 Westport Rd., Kansas City, MO 64111- Get Directions 816-931-4740 Visit Website Find A Table Need a Ride? Dinner menu coming in December or January. Hours: Open 4pm-1am Mon.-Fri.,10:30am-1am Sat., 10:30am-midnight Sun. Having combined a Westport look and feel with a classic French menu, Westport Cafe & Bar is finally charming Midtown with another restaurateuring masterpiece. Directions & Where to Stay Download the app!