The River Market has various restaurants and some shopping just on the other side of the river. Saturday and Sunday they have a year-round farmers market.
Weston is a cute historical town 10-15 minutes away from the venue with knick knack shops, restaurants, wine shops, etc.
The Kansas City Streetcar (more like a bus) does a loop through downtown Kansas City and is free to ride
We love Scott's Kitchen. You can get straight up BBQ or you can get a BBQ burrito/taco fusion. Only open weekdays 7:00am-6:30pm