Wales is probably the closest area to you. would suggest that you have a look at v-g Backpacking site: v-g backpacking , which has lots of information.
In Snowdonia the Carnedds and Moelwyns have plenty of good spots, where you are unlikely to see many other people. A bit further South the Rhinogs, Arennigs and Arans are relatively unfrequented. Beware in the Rhinogs, distances may seem short, but it is very hard going.
One trip I fancy doing myself was originally described by Showell Styles and goes from Prestatyn to Barmouth. There is a post of the Outdoorsmagic forums describing it here: Showell Styles walk .
Ian.