This is a three-stage trip.
Maen Gwyn - N 52 35.448 W 003 50.863
Start at the Co-op in town where there are some large quartz boulders outside, to the left and to the right of the carpark entrance. They may look like supermarket art, but have been there for longer than most of the buildings in Mach - since 1597 at the latest. Indeed, the street is named after them: Maengwyn means 'white stone' in Welsh.
While you're there, make a note of how many boulders are to the right of the car park, and how many are to the left.
Maen Llwyd - N 52 35.449 W 003 50.537
Machynlleth has its very own Bronze Age megalith, 'Maen Llwyd' ('grey stone'). This stood on its own in the middle of a field until a housing estate was built around it. It was moved an unknown distance and re-erected with a plaque some time later. Its current, rather incongrous, location is in a cul-de-sac of this housing estate.
Have a look at the plaque - in what year was the stone re-erected?
Gorsedd circle - N 52 A5.46B W 003 50.CDE
A = total number of white stones in part 1; B is the number of stones on the right of the carpark entrance; C is the number of stones on the left of the car park entrance; DE is the last two digits of the year that Maen Llwyd was re-erected +5. You can probably find this site and have a look for the cache without knowing the co-ordinates, but the other spots are worth a visit and are on the way.
This is your final destination. It might look ancient, but this circle dates from around 1937. It is one of many permanent Gorsedd circles erected for the yearly National Eisteddfod held in locations around Wales, and plays an important roll in these ceremonies.
Dillwyn Miles describes their layout in The Royal National Eisteddfod of Wales:
The circle consists of twelve stone pillars, sometimes hewn from a local quarry, sometimes gathered from the fields, or brought down from the surrounding hills. A large, flat-topped stone, known as the Maen Llog (the Logan Stone), lies at the centre of the circle and provides a platform from which the Archdruid conducts the proceedings. Facing it, at the east cardinal point, is Maen y Cyfamod (the Stone of the Covenant), at which the Herald Bard stands, and behind this are Meini'r Porth (the Portal Stones) which are guarded by purple-robed Eisteddfod officials. The portal stone to the right of the entrance points to sunrise at midsummer day, while that to the left indicates the rising sun at midwinter. The shadows thrown by these three stones form the pattern /|\ symbolising the ineffable name and signifying the rays of the divine attributes—love, justice and truth."
One year and a day before the Eisteddfod is held in a particular community, it is formally announced from the local Gorsedd circle. In 1937 it looked like this:
On a visit here in 1910, a commissioner for the fascinating "inventory of the ancient and historical monuments of the county of Montgomery" [link] noted that nearby is:
A spot, with a natural outcrop of rock, where tradition has it that Machynlleth markets were held during an outbreak of plague, the money used in barter being washed in the adjoining brook, called Nant yr Arian. [trans: money/silver brook]
Interestingly, during the same vist he looked for the Maen LLwyd in its field and couldn't find it.
Bonus: Machynlleth Really Does Rock, aka 'Stairway To Heaven'
Back through the town and across the Dyfi Bridge, there is a beautiful and steep road known locally as 'Stairway to Heaven', about 200 yards on the right on the road to Aberdyfi. Near the top there is Bron Yr Aur cottage, where Robert Plant and Jimmy Page of Led Zeppelin wrote and recorded much of Led Zeppelin III. If you've time, it is a beautiful walk and can be the starting point for much further excursions.