I live nearby and know it well. Where to stay and what to do depends on what you are interested in doing. The major towns/villages are:
Kendal - gateway to Lakes. The most town-like of all of them. Good for shopping & Kendal Mint Cake of course. Nice little ruined castle which you can walk up to in a few minutes from the town.
Windermere/Bowness-on-Windermere - Effectively 2 towns, Bowness is small, quaint and touristy, situated right next to the Lake. About a mile up the hill is the slightly bigger town of Windermere with more of the standard and larger shops. Lake Windermere boat cruises leave from the shoreline at Bowness.
Ambleside - About 10-15 minutes drive from Windermere, Ambleside is probably the busiest and most touristy of the Lake District towns, but still very nice. Ambleside also by Lake Windermere, you can take boat trips and also hire boats from the shore.
Grasmere - A small village on Rydal Water. The two highlights are Dove Cottage, William Wordsworth's cottage (which is a really great place to visit even if you aren't a poetry fan), and the Grasmere Gingerbread Shop, housed in the tiny old schoolhouse. It makes the nicest gingerbread ever, made to the same secret recipe for about 200 years!
Keswick - Another quite big town, this one further north than the others. On the shores of Derwentwater. Lots of nice shops, B&B's & places to eat, along with a few eclectic but fun mueseums (Cars with the Stars & the Cumberland Pencil Museum).
Hawkshead - Nice little small town just across the lake from Windermere (easiest way to get to it is from Windermere by ferry - there's a passenger & a car ferry). Beatrix Potter's home, Hilltop is near Hawkshead and well worth a visit, as is Beatrix Potter World in Bowness.
If walking's your thing, take your pick from the big fells - Scafell Pike, Helvelyen, Coniston Old Man, Skiddaw...