Nope, not sure if there is a site on Grand Cayman... not available to the public at least.
This is a neat site though, requires Quicktime (and broadband, unless you let it sit). It's a satellite derived radar image, updates every 2 to 3 hours... worked very well with Dennis.
http://trmm.gsfc.nasa.gov/trmm_rain/Events/latest_small_auto_pr_slice.qt
That quicktime loop is for the Super Typhoon Haitang...