In my opinion you can't beat Dartmoor. I love walking there, although it can be very hard if you choose the wrong spots, so for starters, avoid the western ranges. The terrain is very difficult and the landscape sufficiently featureless to make navigation difficult. However, once you're feeling confident, there is some wonderful 'lone' walking to be had there, in fact I've worked out a 3 day route that I intend to do sometime over the ranges.
As a starter, and I've mentioned this briefly in another thread recently, try the 2 Moors Way. This starts at Ivybridge, and you could walk to somewhere like Drewsteignton with a couple of nights out on the moors. The 2 Moors Way has multiple routes, allowing those who want to stay out on the moor to do so, while giving options that enable you to stop at some of the villages. For example when I did it, on day 1 I walked from Ivybridge to Holne, stopping at the excellent Church House Inn. Proximity to villages like this is ideal, since it does give you 'escape routes' if things go wrong. For more detail there's a webiste, and the route with alternatives is on the OS map.
Also, as I pointed out recently, the NPA does allow wild camping.
S.