Warwick Historian, Joe Chick, has been involved in a project for The Victoria County History who have made their content available through an app called A History of English Places, which is accessed through a first-edition Ordnance Survey map that pinpoints your location. To demonstrate the app in use, Joe designed a series of walking tours of local history sites that includes Kenilworth.
There is a nice Circular Walk Around the back of the Castle and the Pleasance.
There are also nice walks along the Kenilworth Greenway. Some sections of the may be closed for HS2 construction.
The Kenilworth Footpath Preservation Society have a number of great walks on their website.