In KC there seems to be a "world famous" steakhouse on every corner and, indeed, there are plenty of good places to dine. The Capital Grille would be my choice for the best of the best.
Not far from Country Club Plaza, the Capital Grille is a high-end steakhouse. You won't feel comfortable in shorts and sandals, but you don't need to wear a suit and tie either. It's a great place to impress clients or for a romantic night out. (The bar's a hopping joint.)
As I said, it's high-end and you pay for it, BUT you also get what you paid for and then some. Excellent menu and wine list. GREAT steaks and the level of service you would expect at a fine dining establishment.
I try to eat here every time I stay in KCMO. It's always a treat. I like to make my best clients feel special and, at the Capital Grille, they do.