The approach to Parnitha from Athens goes through the outlying suburbs which are dreary but once you start the climb traffic is light on weekdays and views are rewarding. A better way of going is to approach from the north, above Kifissia, via Varibobi (Varibombi) and Thrakomakedones, though the way is difficult to find and all the maps I have seen are inaccurate, so you will need to ask. Once you start the climb there are numerous hairpins as the road goes up the mountainside. The gradient on the climb is about 8% most of the way. There is a hotel on top and a cafe but the general atmosphere is rural, and it is possible to make a pleasant circuit of the mountain top.
Parnitha is part of a larger mountainous area and rough roads lead away down gorges from close to the summit. Another climb in the same mountain chain, a little to the west of Parnitha, goes via the village of Fili to Stefani and upwards to a quiet pass at about 500m. The road ends here despite what most maps say but it is possible to continue on roughstuff paths; eventually you reach quite reasonable unsurfaced roads and these afford an alternative route to Thebes, cutting out some fairly dull country to the E (see Diary of a Greek Tour).
I have some pictures of cycling in Attica.
West of the Thessalian plain you come to Delphi and also Mt. Parnassus, the home of the Muses, which is an excellent cycling area. Here's a description of the area which I wrote in 1989.
From just W of Aráchova (plenty of hotels), which is at 900m, you climb over a col at about 1100m and then emerge into a flat plain between mountains. You pass the turning to the ski centre on your right. After about 20 km the road rises through woods to a second pass at about 1200m, and then descends quite steeply, with fine views, through the village of Eptalophos to reach the plain. Here you join the main road for a few miles before turning off to Amphikleia, which is the starting point for the return crossing of Parnassus.Amphikleia is quite large and must have a restaurant, though I didn't look for one. There is a good spring just above the village. The road to the ski station goes through beautiful country and is very quiet (July 1989), but is probably the hardest sustained climb (18 km) I have encountered in Greece. The surface is fairly good apart from one section of corrugated concrete. Talk of a ski centre may suggest the kind of concrete horror you find in the Alps, but in fact there is nothing there at all apart from a car park (empty) and a road that spirals up a conical hill for about 100m. The ski centre is not the summit, but after this point the climb becomes easier. There is a distinctly Alpine feel to the mountain at this point. I estimate the height at about 1550m.
I passed a number of tavernas in the mountains but all were closed.
Unfortunately, to approach the Peloponnese from Athens you have to traverse the unpleasant and fume-filled region of Elefsis (Eleusis), but this can be avoided by taking the ferry from Piraius to Monemvasia, in the south of the Peloponnese. Alternatively, there is a district (suburban) railway to Corinth and stations along the way and this will take bikes. (See the email from Judy Allfrey in the General section (Athen Airport.)
A little to the N of Tripolis is the ancient Arcadia; see Map 1 and Map 2 for some routes around Stemnitsa which I've enjoyed. This area is in the Mainolo mountains, at heights of 1000 m or more. I have some pictures of the area.
Stemnitsa is now being actively promoted within Greece as a good place to visit. This is a mixed blessing, I suppose, but even so, the minor roads in the region are still quiet even in August. The two roads into the valley below Stemnitsa are now tarmac. So, too, are many other roads in the area, and this is indicated on new roadside maps which seem to be reliable. However, the road from Psari ('Fish') to Servos is still roughstuff, though not demanding and all of it easily ridable on a touring bike.
There is an attractive climb to the ski centre, or at least to the 1650m pass just below it, on the road S of Vitina. There is a false summit just before the pass; the climb is moderately steep up to this point but thereafter it is easy.
I found a peak at 1335m off the road to Vlongos, just W of Zatouna. However this was steep and difficult roughstuff, not at all ridable going up and only partly ridable coming down.
Pelion is quite different from most of Greece: densely wooded, at least in the centre, and well watered. The road mostly follows the contours but there is an 1159m pass above Khania. From the E. it is a steady climb on a good surface; the W. approach, from Volos, is steeper. There are beaches on the coast but you would have to lose a lot of height to reach them. If you camp wild in Spring (strictly speaking, illegal) you may be serenaded by nightingales.
Recommended routes here are the road from Ioannina to Kalambaka, which includes the above-mentioned Katara pass; the minor roads to the east of the main road between Agrinion and Ioannina, which are very quiet and scenic and where I saw large snakes sunning themselves; and the road from Karpenisi to Agrinion, which is scenic and has four passes at about 1400m. (See my Diary of a Greek Tour for more details.)
You can reach the Pindos from the south (see my Diary of a Greek Tour for an account of this) or alternatively you could fly to Corfu and take the ferry across to Igoumenitsa.
A number of ferries connect the island with the mainland; most leave from the fishing port of Rafina though there are also crossings at Ayia Marina and Oropou. There are good rides to the south (Karystos), with a 400m col S of Kapsala. The area around Chalkis is heavily built-up and carries a lot of traffic, but as you go further north things get much better. At Ayiokambos there is a ferry to Glypha on the mainland.
I once took a roughstuff route from Istiaia through the mountains to Rovies on the coast. It was especially beautiful country, remote and wooded, but rough in places and the way often difficult to find, with no one in sight to ask. From Rovies there was a fairly good dirt road along the coast, on which there are fine sandy beaches, empty too.
Corfu can be approached by air or by ferry from Venice and is a good place from which to reach north-west Greece via the ferry to Igoumenitsa.