Good bus service along the main Windermere-Ambleside-Grasmere-Keswick road, also between Penrith-Keswick-Whitehaven. About 5-10 per day from Penrith to Patterdale, Windermere to Patterdale, Keswick to Borrowdale and Keswick to Buttermere, Ambleside to Langdale and Ambleside to Coniston. You can get round pretty well, in other words, though not to Wasdale, Mardale or Ennerdale
So, obvious places to stay are the hubs of Keswick or Ambleside. Penrith is the rail-head for the former whilst you reach Ambleside via the mainline to Oxenholme, then local train to Windermere and, finally, bus. A crazy way in is the train to Ravenglass, then the narrow gauge to Eskdale, which takes you up to some of the wildest country, though with no onward bus connections.