I live in KC and believe it or not work for Worlds of Fun (plus run an unofficial site on it for 10 years!). Don't stay in Legends West, stay downtown, the Hyatt is nice and is in the center of everything. Legends is NOT what it is cracked up to be, atleast not yet. Its pretty much a stamped out outside shopping area, there is not a whole lot unique about it (except T-Rex which is decent).
Also if I had a choice I would go to Oceans any day over Great Wolf Lodge.
BBQ, what someone said about Arthur Bryants is true, you either love it or hate it, I would recommend Jack Stack BBQ, if you stay at the Hyatt there is a walkway to the Union Station and then from the Union Station to the Freight House District which is were Jack Stack is located. It's a nice restaurant with WONDERFUL food. the prices arn't to bad either maybe $10 for an entree. If you are looking for something more "saw dust on the floor" variety, my favorite is Rosedale's on Southwest Trafficway. Gates & Sons is also good too, there is one near the Plaza I believe.
The Plaza is a shopping experience you really should not miss. As opposed to the Legends (which everyone goes crazy about but again I just don't get) it is very unique, the architecture as I am sure you have heard is modeled (more directly copied) off of Barcelona, Spain. Lots of unique shops,, all upscale, you could easily spend all day there. I can't really recommend any good restaurants there though as the only one's I have eaten at are Cheesecake factory and a few of the tiny eatries. I used to love Winstead's though, I havn't eaten there in awhile but they used to have great steak burgers and milk shakes, its right off of the plaza on Emmanuel Cleaver Blvd.
Within walking Distance of the Plaza is the Nelson-Atkins Museum of Art, wonderful art museum, it's claim to fame is that is does have one of the finest collection of eastern art outside of the east. Plus of course it does have a good collection of Thomas Hart Benton and a WONDERFUL Henry Moore collection (Abstract sculpturist).
Of the amusement park variety of course there is Worlds of Fun/Oceans of Fun. Worlds of Fun is a Cedar Fair park which means if you have a Cedar Fair park near you (see cedarfair.com) get a Maxx pass and it will get you in free. Discount tickets run the gambit. The cheapest ticket available is from Price Chopper stores I believe they still sell them for $27.95 if you let me know where you will be staying I can probably figure out the closest one.
Regular Admission is $37.95, you can get $7.00 of admission with a Pepsi can/or
AAA membership card, $5.00 off if you drive a Toyota (discounts cannot be combined)
All the discount options are available online:
http://www.worldsoffun.com/public/news/special_offers.cfm
If you are wanting to do both parks you might want to look into the Ride & Slide option to, there is a walk thru gateway that connects both parks.
As far as the parks themselves. First I am biased, this is my home park and I love it dearly, obviously I work there isn't it obvious.

It is not a massive park, but it is decent sized, Mamba, Patriot, Spinning Dragons and even now Timberwolf are all very good examples of their types of roller coasters. If you ride Timberwolf ride in the front seat, or the first seat of the second car (row 3), you will get beat up everywhere else. Mamba's best seat is either the back, or the 3rd row of the first car. Patriot is good everywhere but it is especially good in the first row and the last row. If you are into thrills Detonator may look like your average space shot but it is the best out there.
The park itself is clean, landscaping is above average for an amusement park/theme park, quite a bit better then a Six Flags park. Staffing is usually nice. Overall it is a nice park, and I would pick Worlds of Fun over a Six Flags park ANY DAY.
Sorry for the long post, hope this helps you out!
Jennifer