Best location in lake district UK

Look for a Farmhouse B and B. If you bring up a map online of the Lake District some will show you accommodations in the area. You can then tag them and look at their details. We stayed in one near Kendal, but that was a while ago. They served breakfast and an optional dinner. We were there in the Autumn, so it was quite lovely in a wooded location. The hotels by the Lakes cost more, of course. I'm sure you will get more current details, but I'll just start the ball rolling.

Not a town per se, but I spent 3 nights at The Swan Hotel at Newby Bridge last year. Beautiful location and history as a coaching inn. Food was excellent—even if you don’t stay there, can recommend dining there.

https://www.swanhotel.com/

In the Lake District you simply aren't going to find a quiet town during tourist season.
I don't know what you mean by quaint and authentic. Every town and village is authentic in that it is not Disneyland. It existed before mass tourism, and would still exist and thrive without the burden of that mass tourism.
Each town has a back history which over 90% of tourists never explore.
In particular most places in the area would do far better and far prefer it without car - centric tourism. People who won't get out of their cars and use the excellent public transit. It is a major and growing topic in the area.
Actually in the area Hawkshead may be the best fit as the little village centre is essentially traffic free, you park on the edge of the village and walk a couple of minutes. Just outside Windermere the village of Staveley is quite a good fit. Just outside Keswick either Braithwaite or Threlkeld.
In terms of towns then Penrith, Kendal or Cockermouth, or Ulverston on the southern fringe.
Also two days is only ever going to be the edited highlights of the area, it is nothing like long enough to properly explore and get off the beaten track.

Hi Kim -

I agree with Stuart’s suggestion of Braithwaite, but you might also consider the hamlets of Rosthwaite and Seatoller in Borrowdale - they are really quiet. Bassenthwaite is small and slightly off the beaten track and in the southern lakes I have a soft spot for Coniston, which can get undeniably busy but feels away from the main bustle and anywhere up the Langdale valleys is worth seeking out in my humble opinion. I’m thinking of Elterwater and Chapel Stile for instance.

Ian

Since you’ll have a car, if you pass by Grasmere, stop by The Grasmere Gingerbread Shop. It was cash only. If you like sticky toffee pudding and are in that area, stop at the Cartmel Village Shop.

While we stayed in Keswick there were a few villages that looked like they’d be nice to stay in. Unfortunately, during our few days in that area it seldom stopped raining so we didn’t walk around as much as we would have liked.