Suggest you tap into the Find Crags section of the Logbooks page and and zoom on Cornwall. That should take you to literally hundreds of great trad sea cliff routes and bouldering. Sport is limited to a couple of quarries on Bodmin Moor.
Yes, loads and loads! Get yourself a copy of West Country Climbs by Rockfax for a good selection of the best and most accessible routes. I presume you have a rack, ropes etc? Might be a good idea to borrow an ab line if you're feeling like doing some seacliff climbing. Check out Commando Ridge for an epic VDiff experience.