ISO Destination idea for nature and history

This link might provide answers. https://www.travelhackergirl.com/white-cliffs-of-dover-walk-a-day-trip-from-london/

You can also follow the Thames River Path for miles and miles.

Take a look at the 3 and 4 night walking programs offered by HF Holidays at the South Downs, Exmoor, Cotswolds, and Yorkshire Dales. Price is all -inclusive of room and board, plus transport to trailheads and guiding if you book the “ guided” option. They provide clear directions for getting to the manor house by public transport ( generally train plus short taxi ride).

https://www.hfholidays.co.uk/holidays-and-tours/3-night-south-downs-self-guided-walking-holiday

https://www.hfholidays.co.uk/holidays-and-tours/3-night-exmoor-guided-walking-holiday

https://www.hfholidays.co.uk/holidays-and-tours/3-night-cotswolds-self-guided-walking-holiday

https://www.hfholidays.co.uk/holidays-and-tours/3-night-southern-yorkshire-dales-guided-walking-holiday

Page through the photos to see the type of landscape and features offered from the walks. The first two are near the sea with ocean views possible.

ISO? What is it?

ISO = In search of

An organised trip like HF Holidays would be great. It’s not always easy to get to rural areas without a car.

Assuming you are going to be using transit. not driving, York is a great base. You can use the Coastliner series of buses to explore the North Yorkshire Moors and the train from York to explore the area around Harrogate and Knaresborough supplementing that with the very good local bus network.
Harrogate or Knaresborough might actually be better towns for you- Harrogate even has direct (no change) trains from London KX on LNER.
Alternatively you could base yourself in Leeds or elsewhere in Airedale like Keighley (for Bronte country) or Skipton. They have a once a day direct evening peak service from KX, but 1/2 hourly connections into local trains at Leeds.
There is a lot of stunning countryside to explore from Skipton and Keighley (with good local bus networks). You also have access to Hebden Bridge, Ilkley.
Skipton has a good local museum, and if you go up the Settle/Carlisle line one day the Folly Museum at Settle is also good- little known outside the area but good. Skipton also has a thriving street market, a Castle and canal boat trips (on the Leeds-Liverpool Canal). Back down the rail line towards Leeds you have the well known village of Saltaire. In Bradford there is the National Science and Media Museum. The main museum may be closed at the moment but the Pictureville Cinema there is still open, which now has one of the very few Cinerama screens left in the world. There is also much else to explore in Bradford.
Bradford Interchange also has direct trains from London KX on Grand Central Trains, so is another worthwhile base to consider.

Thank you all so very much! I appreciate your willingness to share your time and expertise.

I will research the organized tours today and also look into Harrogate, Bradford, Skipton and the other areas with good bus networks suggested. Thanks also for the suggested blog post. I’m bookmarking that for further research and as a possible day trip from London.

How nice that the OP has returned and said "Thank You". We don't see that very often.

Jhk8080, have a great trip!
And I second Claudia's recommendation for a walk on the Thames Path. It runs through London and way out past Windsor, Oxford, and beyond. The part that's in London makes a good stroll along the riverfront, passing pubs, landmarks and more.
https://tfl.gov.uk/modes/walking/thames-path

On the GoJauntly App, in partnership with Transport for London:
https://walks.gojauntly.com/collections/tackle-londons-thames-path-162

https://en.wikipedia.org/wiki/Thames_Path

The Capital Ring Walk is another great walk in London.
https://en.wikipedia.org/wiki/Capital_Ring

https://tfl.gov.uk/modes/walking/capital-ring
https://walks.gojauntly.com/walking/gb/england/greater-london

Rather than head north, have you thought about Kent/Sussex for your four days? There are some lovely villlages and small towns, along with castles (Bodiam, Penshurst, Scotney, Hever....) There is Pevensey (ruined castle) whereWilliam the Conquer landed in 1066 and Battle Abbey which was the site of the Battle of HAstings. There is the Bluenell Steam Railway or the Romney, Hythe and Dymchurch Railway. Places like HAstings have an interesting history, particulry along the Stade with the fishing boats and fishing sheds. There is Deal with its ruined Castle and of course Dover CAstle... The South Downs and High Weald don't appear on the usual tourist tick list and are quiet and unspoilt. Many A roads are narrow with trees meeting above them.

A bit further aeway is the Weald and Downland Living Museum near Chichester ( attractive with Cathedral and remains of a Roman Palace) which is one of the best open air folk museums in the country with old buildings brought and reassembled on the site.

Rye with its smuggling heritage is delightful as is nearby Winchelsea. Romney Marsh and Dungeness are very different and popular with birders.

Rebecca, thank you for the additional recommendations, especially the Go Jauntly App. I downloaded it and have been having a lot of fun with it already.

Wasleys, I’m considering going south. I’ve never been south of London and it would be less transit time from the city. The desire to go north stems from a trip in 2018 when I spent a few days exploring around Newcastle, Durham, Alnwick, etc and loved everything so now I want to explore more. So many options, so little time! If only all of life’s problems were so pleasant.