Exploring England outside of London

Firstly I would recommend that you look at the thread about areas of England that Americans may not be aware of for some ideas of where to go.
Whether you need to hire a car will depend on where you go and what you want to see. If you're going to many cities e.g. York, Oxford, Bath, Liverpool, Manchester etc then a car will be an expensive liability. You will either be able to walk around and/or use local public transport.
If, however, you intend visiting rural areas like the Cotswolds (if you must), the Lakes, Yorkshire, the Peak District, Northumberland etc etc then a car will be a big advantage.
Lyft does not operate in the UK. Uber does but only in the main towns and cities and generally not in rural areas.

Hi, tcultivate13 - Johnnew52 has an excellent idea about reviewing a recent post that covers many interesting and off-the-beaten-path destinations outside of London. Here is a link to it - it has some wonderful ideas in it. https://community.ricksteves.com/travel-forum/england/the-places-that-the-north-americans-have-never-heard-of

The train combined with bus can pretty much get you wherever you need to go as long as you have some time flexibility. I’d encourage you to pick a focus for your trip. Don’t try to “see it all.”

We rented a car and toured from Salisbury to Canterbury last Fall. Here's a link to my Trip Report if you're interested. https://community.ricksteves.com/travel-forum/trip-reports/trip-report-the-south-of-england
At first we thought about only having a car for part of the trip, but the more we investigated, we determined that some days the train as going to cost more per/day than a car, and some places were not going to be easy to get to.

Highlights for us were Salisbury and Canterbury. Especially liked the docent's tour of the Canterbury Cathedral and the early morning inner access tour at Stonehenge.

To begin with, it might be useful to define/clarify the question.

By London, do you think of Central London, such as zone 1 of the Transport for London? Or do you refer to London within Motorway M25? or do you refer to Transport for London zone 1 to 9 plus special zone?

I'd argue that within M25, there are a lot of good natural attractions, served by public transport under the networks of Transport for London.

Forests /Heath:

• Epping Forest- https://goo.gl/maps/wcMXV3fUG433eXAv6
• Ruislip Woods - https://goo.gl/maps/a39MJvkAD4xfSSiR8
• Wanstead Flats - https://goo.gl/maps/VoTJrxy6JT1amom67

Both Epping Forest and Ruislip Woods are ancient forests.

Parks in suburb:

• Osterley Park https://goo.gl/maps/Ci5118RCVqfy2xrv5
• Richmond Park https://goo.gl/maps/diBvnfnBxdYWBBV46
• Bushy Park https://goo.gl/maps/U2DzLB2bHSMYaGuZ8
• Hampton Court Park https://goo.gl/maps/y2TBCx9W2CCby2NX7

These parks are huge with many walking routes. There might be some local resident walk group which welcome walk-in.

Canal - Grand Union Canal

The Grand Union Canal links London to Birmingham, passing through
rolling countryside, industrial towns and peaceful villages. It is our
longest canal, the ‘trunk route’ of the system, and helps thousands of
people to live healthier, happier lives.

https://canalrivertrust.org.uk/enjoy-the-waterways/canal-and-river-network/grand-union-canal

https://www.artfund.org/explore/map-search?tags=National+Trust&type=all&query=
OR
https://www.artfund.org/explore/map-search?tags=Gardens+%26+outdoor+spaces&type=all&query=

Another good value for money resource you want to look into is the National Art Pass attractions. Even though the title 'Art Pass' may seem to suggest that only museums and galleries are covered, there are quite a number of historic houses under National Trust and English heritage included.

National Art Pass offers 3 months trial from time to time, which only costs 15GBP. The Art fund offering this pass is a charity, so the subscription goes entirely to the art fund, supporting upkeep of heritage sites and museums.

Within and near M25, there are lots of good spots to visit.

• Hughenden - home of the first minority ethnic Prime Minister Disraeli. You can reach there by train (station: High Wycombe) or take Metropolitan line underground to Uxbridge and change to public bus to High Wycombe
• Ham House - a National Trust historic house open all year round (around Richmond area)
• Red House - home of William Morris, a key figure of the Art and Crafts movement (train station: Bexleyheath; zone 5/6 of Transport for London)
• Waddesdon - chateau of the Rothschild family
• Eltham Palace - Art Deco House

In terms of train rovers, check http://www.railrover.org/

Outside London, I think the Southern Daysave offers the best value for money and the best access to the biggest varieties of attractions. It primarily serves East and West Sussex, which have developed modern tourism since at least Victorian times. http://www.railrover.org/pages/southern-daysave.html

If you form a group of 4, it costs 47 GBP in total, i.e. 11.75 GBP per head. It offers unlimited rides on the Southern trains, which runs from Victoria and sometimes London Bridge station, to Southampton/Portsmouth and Rye/Ashford International. If you need local bus connection from rail station, get a plus bus ticket https://www.plusbus.info/

Many interesting towns along the line: Chichester, Hastings, Bexhill, Burgess Hill (to visit Ditchling) and Rye. These towns are mostly walkable.

You can also get good value out of these rovers
Thames Branches day ranger

• Windsor, Henley on Thames, Cookham and Marlow

http://www.railrover.org/pages/thames-branches-day-ranger.html

Kent Rover (3 consecutive days)

• Dover, Whistable, Margate, Cantensbury

http://www.railrover.org/pages/kent-rover.html

I think you're putting the cart before the horse. First, figure out where you'd like to go and then figure out the transportation.

A car of course would give you the most freedom. But you'd be amazed how combination of train, bus and even small van
one day, tours can get you into a lot of rural areas.

Where outside of London do you wish to travel to?

Are you thinking the Cotswolds? The Jurassic coast?
Epping Forest? Brighton? Seven Sisters? Cambridge?

If you provide intel posters can suggest “ best way to get there.”

The OP has not come back to post here in almost 3 weeks.
I think they've forgotten about this thread.