One of the best places I know to look for them is Castlerigg in Cumbria.
Castlerigg Stone Circle (NY 291236) standing within a natural amphitheatre formed by the surrounding fells, is believed to be one of the earliest circles, possibly constructed as far back as 3,000BC. There are 38 stones in the circle, 33 of which are still standing. A further 10 stones are arranged to form a rectangular enclosure on the SE side. The average diameter of this slightly flattened circle is 30 metres.
According to Prof. Alexander Thom's 'Megalithic Sites in Britain' the stones of the ring show seven solar or lunar declensions, four of which cross in the centre of the circle.
As an occasional fell-walker, I have long been aware that the circle stands in direct alignment between Skiddaw and Hellvellyn. In fact, on my first visit there I found that two of the biggest stones in the circle, numbers 13 and 38, form a perfect alignment between the two fells. How, I wondered, did this tie in with the astronomical alignments?

Plan of Castlerigg Circle, after C.W. Dymond (with different numbering system).
The Skiddaw/Hellvellyn alignment runs from stone 38 to stone 13 through the centre of the ringcairn. The tall upright, stone 13 pictured on the right, indicates Hellvellyn. The two stones in front of it echo the shape of the two hills in front of Hellvellyn.

Around 1980 I visited Castlerigg to see if any of Thoms' alignments married up with the landscape alignments I had marked on my map. They did not, but I spent a long time in the circle looking at the alignments of stones and distant hills till eventually I drifted into the north-east corner of the circle where this sort of this seemed to work better. Tired of carrying my rucksack around with me, I dumped it on the ground and walked round, lining up stones and hills, at no time needing to move more than a few yards from my rucksack to do this.

After a while two German girls appeared in the circle. Armed with archaeology books and leaflets they walked round the stones, till suddenly one of them pointed in my direction and both of them converged on my rucksack. I watched with interest but soon realised it was not my humble swag the girls were looking at, it was the faint circular feature surrounding it, an indentation about the circumference of a hammer-thrower's circle. I had never noticed this when I dumped my rucksack on the ground, but the girls had the feature marked on their National Trust leaflets.
Now the strange thing about this indentation is that, even yet, no one knows what it is. The most common archaeological guess is that it is a Bronze Age ringcairn, levelled by 19th century ploughing in the circle's interior. In 1885 Benjamin Williams reported traces of three cairns inside the circle but since then the other two seemed to have vanished.

When the frauleins departed, I had a closer look at the indentation, and took compass bearings and photographs. It seemed to me that the full range of stone shape/hilltop shape alignments can only be seen from the ringcairn; it doesn't work as well anywhere else.
Even the rectangular enclosure that has baffled archaeologists for years looks good from this angle because the double row of stones echo the shape of a low ridge of hills in the near distance and a higher line of hills beyond. This enclosure is a bit of a puzzle because its purpose is still unknown and nothing quite like it is found in any other stone circle.

An interesting point here is that the ringcairn is not in the centre of the circle. It is tucked away in the N.E. corner. There is a hint of conspiracy about this. It's as if the builders didn't want everyone to know exactly where the burial was inside the big circle, but at the same time they wanted to be able to find it for themselves. It might not even have been a burial. It could have been some sort of tribal relic or totem, who knows? There are also enough cross alignments with the surrounding hills to ensure that anyone "in the know" could find their way to that very hillside again without difficulty. One way to do it would be to first place yourself in direct alignment between Hellvellyn and Skiddaw, then walk in the direction of Skiddaw keeping your eye on the summit of Blencathra a little to the right. Stop just before the summit goes out of view behind Gategill Fells. (No dowsing rods or astronomical tables required.) This would lead you to exactly the right spot. It could have been done in prehistoric times, and it can still be done today.

Stone 38 in alignment with Skiddaw, stone 1 in alignment
with Blencathra. Taken from the ringcairn.

The method also works at Torhousekie Stone Circle in Wigtownshire (NW 382 565). Though the 19 smooth granite boulders there are graded in size towards the south-east and are unlike the shape of the hills, if you follow the stone/hilltop alignments round you'll find yourself walking the outline of the "D" shaped ringcairn off centre inside the circle. Compared to the stones at Castlerigg, those at Torhousekie look like graded potatoes worn down in an automatic peeler. The skyline is lower and the total effect is rather like a Disneyland Castlerigg, but almost certainly based on the same principle.

My next visit to Castlerigg was years later with the Association of Certificated Field Archaeologists. As an experiment, I positioned the members inside the circle, each facing a different stone and hilltop, and asked them to walk backwards keeping their designated stone and hilltop in alignment. Stopping when our shoulders touched we found ourselves right on the edge of the ploughed-out ringcairn. Slides of the stones and aligned hilltops photographed from the ringcairn, were shown at the 1994 AGM, and members were asked to vote whether they thought the stones had been placed in position to approximate the shape of surrounding hills or not. Twenty-two people voted; 17 thought the alignments were deliberate, 5 did not.
If these alignments were intentional, it suggests that whoever masterminded the layout of the stones did it from the ringcairn. If this is so, then the ringcairn must have been constructed before the circle and is thereby the earliest structure at Castlerigg. It's as simple as that. Castlerigg is a stone circle built round a burial. It is not a stone circle that had a ringcairn inserted later.

Left: Stone 4 from inside the ringcairn. Centre: Stone 4 from outside the ringcairn, but still inside
the circle. Right: Stone 5 points to Great Mell Fell (with ditch-enclosed barrow on top).

Could the stones be aligned to the surrounding hills and to stars in the night sky at the same time? Personally, I don't see how this could be possible inside the confines of one stone circle. With a bit of stone shifting through the ages a landscape aligned circle could possibly have made 'astronomer friendly', but in my opinion the two ideas are mutually exclusive - take your pick! Next time you visit Castlerigg, check it out.

Further Reading

Burl, A. 'Stone Circles of the British Isles', Yale University Press, 1976.
Farrah, R.W.E. 'Mayburgh Henge', Northern Earth. issue no. 85, 2001
This article explains how Blencathra comes in and out of view at significant points of Mayburgh Henge (NY 51922843) 15 miles east of Castlerigg. Farrah suggests that the contours of the entrance to the henge mirror the saddle shape of the mountain and Mayburgh was purposefully oriented towards Blencathra.
Dymond, C.W. 'Transactions of the Cumberland and Westmoreland Antiquarian and Archaeological Society, Vol. V 1881'.
Thom, Prof. A. 'Megalithic Sites in Britain', Oxford Press, 1967
(There is no known astronomical alignment connecting stone 13 and stone 38, but according to Prof. Thom, stone 13 and stone 31 form an astronomical alignment between the Candlemass rising sun to the SE, and the most northerly setting moon to the NW.)

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