Your plan may look good on a map but in fact it is terrible in real life.
Athens is a very big (and in most places ugly) city. It has no beginning or end. You cannot really find a place without people around to set a tent, and certainly an open fire is out of the question all over the Attica peninsula.
If it was summer, somebody would call the police for the fire. Now that is winter you may avoid the police (not certainly) but I cannot think of a pleasant place to set a tent and light a fire. The only pleasant places are the nearby mountains (Parnitha, Imitos, Penteli, Gerania, Pateras, etc).
If you want to circle Athens be prepared to walk around industrial zones and never find a place without (annoying) human presence. I really cannot imagine a tourist visiting Perama unless he wants to see with his own eyes the results of economic crisis in Greece. Perama was a major industrial zone (shipyards) and is almost out of business now. Salamina, once a beautiful island, is now in most places, no more than another low class neighbourhood of Athens. Not much different than Perama.
I would avoid mt Pateras. Its forest was burned a few decades ago and never recovered. I would also avoid for overnight walks, mt Imitos and mt Penteli. They both overlook densely populated neighbourhoods of Athens and I do not imagine the neighbours will welcome somebody lighting a fire not far from their houses.
For one day outings from Athens for these mountains, choose from the following routes (use a ranslator). You can reach the trailheads using the Athens bus network:
For Imitos
http://users.sch.gr/ppapachr/ymittos/main.html
http://users.sch.gr/ppapachr/ymittos2/ymittos2.html
http://users.sch.gr/ppapachr/agiannis-s ... ilaio.html
http://users.sch.gr/ppapachr/kareas-kor ... oropi.html
For Penteli
http://users.sch.gr/ppapachr/Dionysos-E ... omeia.html
http://users.sch.gr/ppapachr/kastritsa/kastritsa.html
Mt Parnitha if far more attractive for day outings or for overnight stays. The mountain has suffered a lot from the fire of 2007, so an open fire is under all circumstances, out of the question. Not even on top of snow. There are 2 huts on the mountain where you could stay. Call them to arrange. Their sites are
http://www.mpafi.gr/ and
http://www.flabouri.gr/.
Camping is illegal in Parnitha but I do not imagine that you would have any problem camping, as long as you are not that visible. You could set a tent at Mola, Limiko, Saloniki, Agio Nikolao, Paliomilesi, Pireza and a lot more places. Look here:
http://www.hellaspath.gr/misc/waypoints.php?mnt_id=45 for the waypoints MOLA, LIMIKO, SAL, AGNIKOL, PALIOMILES, PIREZA.
You could even sleep at the (empty during the winter) fire watchers’ hut (EDASA).
There is an extensive path network. You can find most of the paths here:
http://www.hellaspath.gr/index.php?p=2&m=1&mntid=45.
If you want to do a multi day walk, you could combine (and stretch) these 3 (or more) routes and sleep somewhere in the middle.
http://www.hellaspath.gr/index.php?p=2&m=1&mntid=45#107
http://www.hellaspath.gr/index.php?p=2&m=1&mntid=45#114
http://www.hellaspath.gr/index.php?p=2&m=1&mntid=45#120
You can go at the trailhead using a bus and return to Athens taking the local train either from SFENDALI or from AVLONA.
To finish it:
If you want to see the antiquities (and you should in my opinion), take the bus and go see the antiquities. Visit Akropolis and its museum, the Agora, the National Archeological museum. Take the bus and go visit the temple at Sounio. Find a camping to sleep near Sounio.
If you want to hike in the Athens area, go to Parnitha.
Forget your plan to circle Athens unless you want to suffer for Guinness book purposes.
