I've ridden the Katy twice, the second time we stayed at the Hilton in J-City. It's a full service hotel with a restaurant and bar, It's not far off the bridge, and you get to ride by the Capitol building. They don't mind you rolling dusty bikes through the lobby and on the elevators.
Yes, there's a looooonng 1<% grade heading west.
Katy Trail and Rock Island Trail Elevation Charts (bikekatytrail.com)