Andy ! I live in Plymouth and though I'm not a "carp angler" per se I do know a few good venues available on a day ticket. Bush Farm Lakes near Hatt(Saltash) (ca 10 miles) is very good , esp. the 2 right in front of the farm. The bigger carp are there. They average doubles but there are 20s too. They respond very well to floaters - though actually hooking them ain't easy. Keeping your line off the water is often important ...ie fish right close in. Despite being quite busy , its often very quiet at night. Flavoured meat etc all score well at night. Daytime or evenings stalking over baited areas close in can be good , often outfishing the hi-tech static approach.
Sundridge Fishery (ca 5 miles)is very small , scenic and pretty easy. One bonus is that it usually has quite clear water . You can often see the fish take!
For a challenge Rackerhayes Fishery at Newton Abbot (30 miles) is a good bet. It has some very large carp and huge tench . It is not a commercial fishery , its a club water.
Hope that at least starts you off. Email me if you've further queries , and tight lines!