Lake District

A lot of places to see and things to do. The GoLake tourist information website is a good start: http://www.golakes.co.uk/

The Lake District is a walking mecca with the hills swarming with fell walkers during holidays and weekends: http://www.golakes.co.uk/adventure-capital/walking-lake-district.aspx
Peak bagging: http://www.lakedistrictpeaks.co.uk/helvellyn.html

Or if you want a less adventurous activity, there is the bunny lady's Hilltop Farm or its "attraction": http://www.hop-skip-jump.com/

The Lake District is NW England. Do you mean you are travelling to the Lake District AND NE England, or is it just a bit of confusion?

Honister slate mine is good. Some really good pubs--my favourites are the Britnnia at Elterwater and the Masons Arms at Strawberry Bank. Blackstone House is a fabulous Arts and Crafts place.

I like the pines of Buttermere on HonisterPass.

If you are in Windemere you must stop at Huddleston's Butcher shop- they sell meat pies - go early which is when the largest selection is there. Honestly it was the best meat pie i've had in my life, and they've won awards for them.... worth it if you are in the area.

In Ambleside, the Old Stamp House has some excellent soups and meat dishes.

Do try to visit Beatrix Potter's home, its very charming and bucolic. You can also take a boat out on the lake from Ambleside.

There are many scenic drive options. Rick's guidebook describes the Newlands Pass route to/from Buttermere, which can be part of a circular route from Keswick. It wasn't on the small brochure map that I had from the Keswick Tourist Office, but they also recommended it and drew it in for me.

If you have a car and want to sleep in the Beatrix Potter neighborhood, then I can recommend cuckoobrow.co.uk in Far Sawrey.

This is also a pretty dense area for finding stone circles, with Castelrigg probably most accessible, but others could be hiking destinations.

http://www.lakedistrict.gov.uk/visiting/thingstodo/archaeologyvisit/stonecircles

http://www.visitcumbria.com/stone-circle/

http://www.historic-uk.com/HistoryMagazine/DestinationsUK/Stone-Circles-in-Cumbria/

If you like literature...
Dove Cottage and Rydal Mount...the homes of Wordsworth.
Brantwood...the home of John Ruskin on Coniston Water.
Hilltop...Beatrix Potter's home near Sawrey.
If you like ancient things...
The Castlerigg Stone Circle above Keswick to the east.
The Roman fort at the top of Hardknot Pass.
If you like to walk...
Go out to Buttermere and walk around the lake - gorgeous!
Walk the path along the eastern shore of Derwentwater with a view of the Catbells on the other side.
If you like boats...
Go out on one of the old wooden launches from the dock at Keswick out onto Derwentwater.
I could go on but those are a few of the things I love there!