Hiya,
We camped on Dartmoor last Friday night, at Fur Tor. Twas windy, but managed a semi-sheltered spot on the E side of the main tor. Nice, relatively remote spot with water not to far away. If you want bouldering tho', you've not much but Fur Tor itself, so probably not the best spot.
I've also camped at Black-a-tor, just 'downstream' of the wood itself, on a flat, possibly damp area (it was frozen at the time). We arrived after dark and left at first light. On this basis you'll not encounter problems on the open moor, but leaving tents/tarps around in daytime may attract unwanted attention.
As several folk have said, open fires are a no no. Twenty odd years ago as yoofs, we used to nick coal from the (then unlocked) range observation huts and settle down to a blazing coal fire (built on a bit of dry streambed). Ah, those were the days!
I've also bivied in Fernworthy Forest, just over the wall on the northern side, again, arrive at dusk and away by dawn.
I hope the weather is kind when you're there at Easter. I'll be in the Cairngorms, where it'll probably be worse!!
Have fun