Major family campsite, but if you've got DCs, woodlands park is great. There's an adventure park attached to the campsite, which is brilliant for never needing to go anywhere. And as family campsites go, not too hideous in terms of kids racing round on bikes/tiny plots etc. lots of nice big fields with big plots if you don't need an electric hookup, or smaller plots in rows if you do need the hook up.
There is a place called Axehayes Farm Campsite thinking about it on that main road from the Exeter services roundabout just before you get to Crealy. It's officially in Clyst St Mary which I suppose is about 15 mins from the centre of Exeter depending on traffic.