Ideas for 2-3 days of walking/exploring outside of London without a car?

I think the south coast is great choice. There are buses that connect points easily. Train to Eastbourne and then day hikes at Beachy Head or Birling Gap?

Thanks! Any suggestions on a good place to stay on the south coast? A good home base for links out to walks?

You could take a South Western Railway train from London Waterloo to Poole then a bus to coastal Studland. Great walks along the South Coast Walking Path. There is good bus service throughout Dorset for tourists and locals in the summer. MegaBus will also take you from London to Poole. We stayed at an old fashioned resort, Knoll House and the Purbeck Breezer bus stops right in front of the hotel. Lots of day hikers used the coastal bus. There were many families there for the hiking, tennis, rustic golf, croquet, swimming pool, horseback riding, kayak rental, historical bunkers and the beautiful Old Harry stacks. They provided golf clubs, tennis racquets and croquet gear. You could take the bus to visit other towns nearby. We booked half board which included breakfast and dinner. It was like a relaxing vacation from our month long vacation.

https://www.knollhouse.co.uk/

Cotswold district!!!!! Besides the Swiss Alps my favorite walking district in the world. It takes about 2 hours by car and about the same by Train/Bus. Car is much better because there are several villages there and you can drive to right where you want to begin walking/hiking. Park your car and you are off. You can cover 2 or 3 villages and in between each day. Drive back to London early Thursday in time to drop off car and catch your train.

Consider training to and staying in Whitsable.

If you head to Eastbourne my friend likes the Royal Victoria Hotel in St Leonards.

Another option via train and bus would be Lyme Regis on the Jurassic Coast.

Or visit the Epping Forest

Or to the Seven Sisters

ideas for car-free breaks https://www.theguardian.com/travel/series/car-free-uk

For the South Downs Way and the Seven Sisters/Beachy Head area, you could look and the maps of the South Downs Way, you could look at the National,Trail South Downs Way website and pick a village on or near the trail so you could walk it both directions from your base.

https://www.nationaltrail.co.uk/en_GB/trails/south-downs-way/

For more ideas in that area, look at the hikes offered in the area by HF Holidays, from their country house neat Thakeham. You could easily duplicate these from your own chosen lodging. Scroll down to the last two days to see the Devil’s Dyke and Seven Sisters hikes. Below the hikes you will find phone numbers for taxi service in the area, which might be useful for getting to trailheads from your base village.

https://www.hfholidays.co.uk/holidays-and-tours/7-night-south-downs-guided-walking-holiday?format=pdf&vid=3434

For possibilities in that and other areas reasonably close to London, I suggest you get a copy of TimeOut’s “Country Walks, Vol 1”. This suggests 52 different walks starting and ending at train stations within an hour or two of London. Some are circular and some are one-way but end at a train station where you can catch a train back to your starting point. Arundel like a possible base for the South Downs area.

Picking up on your comment about the Peak District - yes that is walkable without a car. Catch a train toe Sheffield and then train to either Hathersage, Bamford or Edale. Edale would be top choice, as it is the start of the Pennine Way and there is lots of walking that can be done from the village. Lots of ideas and information here.
Problem may be finding accommodation though.

Hathersage is probably next best with walking ideas here.

We stayed in Chipping Campden in the Cotswolds for six days and used it as a base to visit Oxford, Blenheim Palace and Stratford Upon Avon, as well as the Cotswolds. Check out the Volunteer Inn, great rates, great pub and Indian Restaurant.

You will need a car for the Cotswolds unless you don't mind public transport and walking.