Castle Rock, Calton Hill and Arthur's Seat from Blackford Hill.
You can visit the hills in any order and will probably want to do so over multiple days. No single one of these hills is that taxing on its own but the overall effort required to visit all seven is what merits the terrain and difficulty ratings. There is a seven hills race in June each year where the fastest runners visit all seven summits in well under two hours but you won't have time to stop and admire all the views properly then, nor find any other caches on the hills. If you are interested in the race, their website is here. Wikipedia tells you more generally about the seven hills and the hills individually, as do the other caches local to each hill.
Castle Rock
The first waypoint takes you to the north east corner of the castle esplanade where you can find E at the Witches' Well. This is a cast iron wall fountain which commemorates the place where over three hundred women were burned at the stake accused of being witches. You do not need to pay to enter the castle, unless you want to visit it anyway.
E = number of "I"s in the Roman numeral date at the bottom right of the fountain
Calton Hill
The next waypoint is the trig point on Calton Hill. From here you can see a pillared structure, modelled on the Parthenon in Athens. This is Scotland's National Monument and is a memorial to the soldiers and sailors who died fighting in the Napoleonic Wars. Near here is earthcache Calton Hill which will tell you more about the seven hills in general and this hill in particular.
F = number of pillars (or partly visible pillars) of the National Monument visible from the trig point
Corstorphine Hill
There are two very close by waypoints on Corstorphine Hill and two bits of information to collect. The tower is a memorial to Sir Walter Scott. There’s another earthcache nearby Corstorphine Hill, roche moutonnée. Edinburgh Zoo is also on Corstorphine Hill so keep an eye out for zebras, wallabies and other animals through the fence.
A = number of lines on the plaque on the memorial bench for Catherine Keeble
D = line number (from the top) of the letter F on the side opposite the blank side of the stone direction pillar
Craiglockhart Hill
There are actually two hills here, Easter and Wester Craiglockhart. The seven hills race visits the lower of the two but you can choose which to climb. Craiglockhart campus just by the two hills is famous for its previous use as a psychiatric hospital. The most famous patients were the war poets Siegfried Sassoon and Wilfred Owen. Nowadays it is owned by Napier University.
B = twice the number of uncut metal loops on top of the trig point of Wester Craiglockhart Hill
OR B = the number of metal rings/cylinders in the ironwork of the bench at the top of Easter Craiglockhart Hill
Braid Hills
Braid Hills suggests more than one hill but there is just one trig point that you need to visit and the waypoint is the information pillar next to that. The information disk on top of the pillar has plenty of information about the seven hills and the views are excellent from here. There is another earthcache here Seven Hills Outlook all about the seven hills and local geology.
G = the second digit (not written number) to appear in the grey box in the middle of the information pillar
Blackford Hill
Blackford Hill is extremely popular with cachers it seems as it has many, many caches on it, all worth a visit. You may also pass the Royal Observatory of Edinburgh and their public stargazing nights have an excellent reputation. Edinburgh’s observatory was originally on Calton hill but moved out of town to Blackford to avoid light pollution. Nowadays, Edinburgh University astronomers use a telescope based in Hawaii!
H = total number of words in the first two lines on the plaque on the bench at the top
Arthur's Seat
Arthur's Seat is the highest and most distinctive hill in Edinburgh. It isn't really known where the name came from but many believe it is linked to Arthurian legend. Either way, Holyrood Park which surrounds Arthur's Seat is an amazing place and well worth exploring. There are again many caches here, including one of mine: e for ? The summit itself is an earthcache Arthur's Seat Earthcache.
C = number of stones making up the middle layer of the information pillar
J = number of uncut metal loops on top of the trig point
The Cache
I hope you've enjoyed this tour of the 7 hills of Edinburgh. The cache itself is hidden at:
N55 AB.CDE W003 F.GHJ
You shouldn't need confirmation of your coordinates as each number should be easy to find once you're actually up the hill. I've removed the geocheck link as people were misusing it so please email me if you would like to confirm your coordinates or check anything.
The Bonus Cache
The bonus cache for those who've completed all the 7 Hills of Edinburgh is here. The bonus coordinates are in the 7 Hills cache box both inside the lid and on the base. You'll hopefully get excellent views of all 7 hills from the bonus, which is in the Pentland hills just south of Edinburgh.