I would say either the Intercontinental or the Raphael on the Plaza -

I agree with sunburn.

I agree too, as a personal preference, but as always it depends on what you want.

I prefer the Plaza area because it is simply more beautiful. In addition to the shopping and multitude of dining establishments, the fountains and statues (and in the summer the flowers) make all the outdoor walking around so pleasant.

There's some live music about in the evening, as well as a movie theater on the plaza. It's within walking distance of the Nelson Gallery and the Kemper Museum of Contemporary Art. If you are a tennis buff, there are tennis courts at the plaza.

Raphael and Intercontinental have more "atmosphere" but the Marriott is in a great location too...especially for the art museums. Oh, and Shakespeare outdoors in the summer in the park alongside the Nelson.

Crown Center is also in a nice area, though. Just not where I would personally stay. It's more of a downtown business district type to my mind. That said, it is by Union Station and Liberty Memorial. There is a children's theater, a movie theater and the American Heartland Theater in Crown Center. They have outdoor movies on some Friday nights in the summer. So it is not without its own charms and activities...so take your pick!

I would definitely choose Country Club Plaza. Crown Center is nice enough, but basically its just a mall. CCP has lots of beautiful fountains and the architecture and atmosphere is really nice. There are lots of great restaurants nearby, and a walk along the canal is a great way to spend an evening.

Tracy

I'd get a room at the Raphael with view of Brush Creek and the Plaza. It's a more old fashioned hotel, very comfortable and a European feel. Pleasant walks in the area. No pool. Now if they would just get rid of the goofy cow statue in front.

Crown Center is more modern.

Hi Gapper -
Definitely go to the Plaza -
but I would not recommend the Raphael. I took a tour last week scouting out sights for my honeymoon (staying one night in town and then going to Colo.) and I was not impressed by the Rafael. It was just okay.
The Intercontinental, Sheraton or Marriott would be nicer. I always try a Priceline bid, with 4 star priority, and end up with very nice and reasonably priced rooms. You may try that. You don't get to choose the room, but with a 4 star rating choice you won't be disappointed.
If you wanted to visit Crown Center it isn't far by cab, and I think they run a shuttle from the plaza to Crown C. too... over at the Hyatt they have a revolving restaurant that we go to for drinks and dessert later in the evening - it offers a 360 view of the city. That is worth a visit. (It is a nice hotel in the CC area.)
Also, Liberty Memorial is near CC and is a nice visit. Get there earlier in the day so you can go up in the tower. Spectacular view!!
If you have time, visit the City Market on Sat. or sun. before noon. All diversity of food and people - Great place to people watch and place for lunch - just about any kind of food you want.
If you are driving, and have time I would recommend a trip to Pieropo's in Parkville, MO. Its about a 10 min NW from downtown. I know they would be glad to give you directions. Its my favorite. Believe me, there probably aren't too many restaurants I haven't been to here.
Okay, sorry to make this so long, but I have experienced the good and the bad here, so I just like to share my experiences.
I hope you have a great time whatever you choose.
(I know this is more than what you were asking, but hopefully it'll help someone)