If you'd like to be by the sea, my top tip is Newton-by-the-sea, it's about the quietest most beautiful beach anywhere. There are quite a few cottages nearby if you google , can't work out linking on my ipad.
We've stayed at 4 different Coquet Cottages over the last few years and every one has been fantastic, they're all the same high quality standard and they have free wi-fi and PS2's and stuff for the kids. The staff are really helpful I usually ring up and ask for recommendations and each time they've been spot on. So far we've stayed at Warkworth (very pretty), Newton by the Sea (great beach and pubs) and Alnwick (nice town). I know a few people who've also booked with them and never heard anything but praise so might be worth you trying them.
and we stayed here last year, gorgeous place - tennis courts and every fink! Actually I'm not sure the first place I linked to had wifi, as it was not something we'd have thought about at that stage. This place did - though it could be a bit slow, in being a bit out in the wilds...
I've just looked up the links for the cottages we stayed at which I thought might be helpful, save you trawling round, Sunny CottageLeaholme Cottage and Percy St Our kids loved Sunny Cottage best (stayed twice), OH loved Leaholme bestf but that was cos he thought the Ship Inn was the best pub he'd ever been in!
In the Keilder area we stayed here Falstone Barns it was very luxurious and the owners very friendly. Ideal for Keilder forest area. For more access to the coastal area we stayed here Chatton PArk which was great- really comfortable and large, lots of nice pubs/ restaurants around and we went along the coast every day. Great holidays!