I was just at "Arvest Theater" last weekend. It's really called The Midland, and it's a good venue. Nobody calls it Arvest except people paid to do so.
Where are you staying, and about how long are you here?
Kansas City isn't a good place to roll around uninformed/unprepared. You can go from high end, seven figure housing to slums just by crossing a street. I'd make an "avoid the hood" overlay, but it'd be very complicated.
The area around the Midland and P&L can get pretty crazy at night. There are street criminals downtown, but realistically, drunks are probably the bigger threat around there at night.
For food, the big deal around here is barbecue. It's a hotly debated subject, but most places are good. I'd suggest Oklahoma Joe's and Fiorella's Jackstack as starting points. OK Joe's is solid, and it's more casual. The Jackstack is more of a finer dining environment, but it's not crazy expensive. I'm pretty fond of their lamb ribs, but the local menu item is burnt ends. They're much better than it sounds.
If you want something more homestyle, Stroud's is pretty solid.