Demo summed it up quite well. Choose a location with trees and prepare to wander until hidden, it's pretty much all fair game up here if your careful and prepared to walk around.
Not really able to give true specifics but i will try, for the most part the area is too dynamic due to forestry work and tourism unless you want a location you could be moved on from. There are some very good areas around the duddon valley, coniston water and lake windermere. The safest bet with walking options is probably windermere, near the car ferry, there is a wood full of sweet chestnuts and fungi called heald wood. Towards claiff heights from the ferry there is a place called three tubs tarn that is also nice to sit, very heavily walked but you'll be hard pressed not to find a hang with a view along the walk somewhere. There are some cracking views from heald wood onto windermere.
Avoid grizedale and broughton beck area if looking around coniston unless your ballsy, very heavily worked by the FC and the deer come though at quite some speed. The shorelines of coniston and windermere get patrolled too by either the LDNPA or NT.
I would say the duddon valley but then i am biased, i grew up around there and think it looks fantastic, i also prefer to walk off beaten routes and be away from the tourists. You'll get a hang in
forge/hartley close wood and there is a bothy in/around there to be found and good views. There is another wood with a good view at ulpha a little further up, i think that's church wood. Wallowbarrow gorge i also like, although far more hazardous, limited on where you can get a hang and it can be a real bad walk when wet it has some powerful rapids to stare aimlessly at. Don't get tempted to swim in the gorge though, it is a killer, lots of undercuts in the rocks and that's an understatement, its a bcu 5+ last time i checked. In fact i'll deter you more and tell you how a friend lost his fingernails trying to dig his way out of one of those undercuts... Further up towards dunnerdale and yet more trees and views, last time i was there there where a few decent areas.
Not sure about the northern end of the lakes, there tend to be less trees up that end.
To be honest it's probably easier to pick somewhere on a map, put it forward and see if there is a reason not to use it when it comes to the lakes xD
Hope some of that was useful