There are definitely camping options along the Katy Trail, although they might not all be within one day's hike from each other. Here's a list of
campgrounds along the trail. If you follow that link and go to the bottom of the page, you can use the "Lodging" checkbox to also get a list of B&Bs, hotels, & motels.
I've heard that other campsites will be opening in 2006, but no details yet on where.