English countryside and villages

Stonehenge can be done as a day trip from London.

,I really like York, there's a lot to do there, and its an easy train ride from London.

Dartmoor and Exmoor and Bodmin Moor are in the south west of England.

This is just my personal opinion which you can use to help you decide. If it were me and I just had three full days I would focus on the York area. Nearby you can see the North York Moors and the beautiful coastline running all the way up from Bridlington to Whitby and beyond. You can branch out into the dales where there are lots of little old timey villages. I think Robin Hood's Bay, on the coast south of Whitby, might also fit your description.

You could try to fit in a day trip to Stonehenge (or Avebury, which are other standing stones nearby) from London. It's definitely possible but for me that would be too much considering your other plans. It is a very long day from London.

I'm not aware of any standing stones in Yorkshire but I'm sure others have ideas. Or you could wait for a future Scotland trip and visit the standing stones of Calanais in the Western Isles.

The most accessible standing stones to York are probably the devil's arrows at Boroughbridge (hourly bus from York).
Given your specifications Malton (half way between York and Scarborough) could fit the bill to stay in, one of the stops on the York to Whitby scenic bus over the North Yorkshire Moors- number 2 above.
From Whitby you could take another bus down the coast, may be to Robin Hoods Bay.
If you want a big and impressive stone circle (far more so than Castlerigg, near Keswick) you could take the Settle and Carlisle line in North West England to Lazonby and visit Long Meg and her daughters, either by local taxi or on the Fellrunner Community Bus- but it's the wrong side of the country. I can guarantee no one will be there. One of several unknown stone circles in Cumbria.

Looks like you are trying to do this by public transport. Here is a very different idea.

After you are done with London, take the train to Salisbury (~90 mins). Visit Stonehenge from there, and then take the train to Wareham (~2 hrs). You will probably need one overnight in Salisbury.

Use Wareham as your base for 2 nights. You can visit Stoborough Heath from there - not the most extensive moor, but Enid Blyton used it as the moor for the Famous Five, so it can't be that bad, can it? Also visit Corfe Castle and Lulworth Cove for cute villages, seaside and the lovely ruins of the castle. There is a good (and fun - sit on the top deck if you can) bus service (Purbeck and Jurassic Breezers; morebus) to all these locations (Stoborough heath, Corfe Castle as well as Lulworth Cove) from Wareham. If you have time, go to Durdle Door and walk to Lulworth Cove from there....to get a taste of the coastal path.

Have fun!

Malton is lovely- we just stayed there a few weeks ago. It's on the railway line from York to Scarborough and easy to get to Castle Howard and the coast.

Do a day trip from London for Stonehenge.

York is my favorite city in England. North of York, you can rent a car and drive through the Yorkshire Moors from Pickering to Whitby.
You don't need more than a day in Whitby, but you need 3 days in York.

Who says you only need one day in Whitby?

There is another active thread where 4 days in Whitby is proving to be insufficient to explore all there is in the area.

If you don't like big cities and prefer to spend your time in the countryside, you could skip London. Do what you like and are interested in.

There's a lot more to England than London, as you've decided, so full marks for wanting to see more of the country.

However, with only six days, concentrate on either the south (Stonehenge, Salisbury, Winchester, Avebury, New Forest , South Downs, Dorset with its delightful small villages, the equal of the Cotswolds and is Thiomas Hardy country....) OR head north (York with North York Moors, Whitby etc).

On the train network it is just as quick and easy to get to the north of the country as it I to travel across the south.
If you are prepared to extend your search from English to British ( well Welsh!) have a look at North Wales.
It has beaches of every kind, Snowdonia National Park ( now known as Eryri National Park) for moors and mountains, castles and associated medieval towns like Conwy, steam trains, slate mines to explore as well as its own language and culture.

From London you get there on the train via Chester, a small City with a cathedral, Roman remains and unique architecture in ‘the Rows’. Chester is just over 2 hours from London on the train, which is nothing really. My commute across London used to take that some days!

One word of warning, school half term holidays fall in October so prices can sky rocket in all tourist locations during the holiday weeks.

As a person who likes moors and walking on them and has a thing for stone circles, I can appreciate your interests. 6 days is not long (assuming this doesn't include arrival and leaving day) and you will need to make some choices or spend a lot of time on a bus or train. This means making some choices. London would work well if you added somewhere close so you don't lose a lot of time travelling. For example, while York is only 2 hours by train you have to add in the time to get to the station, wait for the train and then get to your accommodation on the other end. I like Whitby but that will be another few hours so you have lost most of 1 of your 6 days. The person who suggested dropping London for this trip and either going north or south is correct.

Consider London combined with Canterbury, Dover Castle, Salisbury (Stonehedge although Avebury is more interesting) and the white cliffs.

If dropping London, you now have time to see more. If going north, the North York Moors are the place for walks. Robing Hood Bay is good for the coast. You haven't provided the age of your boys, but if they like/liked Harry Potter, consider Goathland whose station was used for Hogsmeade Station in the films and still has a steam train that runs through it. My kids loved it. If staying south, there are lots of towns to consider with fun places (Canterbury, Arundel, Portsmouth).

I suggest making a decision on your direction and start focusing on what you want to see there.